AD-777 738 THE PRACTICAL IMPACT OF RECENT COMPUTER ADVANCES ON THE ANALYSIS AND DESIGN OF LARGE SCALE NETWORKS Howard Frank Network Analysis Corporation Prepared for Advanced Research Projects Agency December 1973 DISTRIBUTED BY KfiTi National Technical Information Service U S DEPARTMENT OF COMMERCE 5285 Port Royal Road Springfield Va 22151 ·•· THIS DOCUMENT IS BEST QUALITY AVAILABLE THE COPY FURNISHED TO DTIC CONTAINED A SIGNIFICANT NUMBER OF PAGES WHICH DO NOT REPRODUCE LEGIBLY Security Clasiitieation DOCUMENT CONTROL DATA - R D rlD 777 73 Q fr -utlr la»«nfir»M«l e Ulf« agjjjf o aftwratl und Indrtlnj tnnolmllon muml am mnlmrmd wh n Ihm oimtmll rrport Im clmmllrd I ORIGINATING ACTIVITY CatpOtmlm malhti 1 2« REPORT SECURITY CL ASSIPlCAT ON 2 CROUP iiclassificd Network Analysis Corporation Beechwood Old Tappan Road Glen Cove New York 11542 None DEPORT TITLE Second Semiannual Technical Report December 1973 for the Project The Practical Impact of Recent Computer Advances on the Analysis and Design of Large finale Net-works DESCRIPTIVE NOTES Typm ol imootI aflrf Inttumirm tlmf» Second Semiannual Report December 1973 » AUTHORISI Lmmlnmmm llrml nmmm UtiUml Network Analysis Corporation » REPORT OATE 7a TOT Aw NO OP PACES 522 December 1973 Sa CONTRACT OR CRANT NO I« Semiannual Report 2B PROJECT NO CARPA Order No 2286 74 •a ORIGINATOR'S REPORT NUMBERtSt DAHC15-73-C-0135 ft 7» NO OP REPS »ft OTHER REPORT NOtSI Any Olhmt nidtm Ihmt mmr ft» mmmlgnmd that rmpoel AVAILABILITY LIMITATION NOTICES This document has been approved for public release and sale its distribution is unlimited II SUPPLEMENTARY NOTES None IS 12 SPONSORING MILITARY ACTIVITY Advanced Research Projects Agency Department of Defense ABSTRACT New research results on the following major questions are reported ARPANET growth Impact of Satellite channels on packet network cost and performance terminal oriented network cost and performance packet switched network design routing in packet networks large network computations broadcast packet system considerations routing and acknowledgement schemes for broadcast systems spread spectrum considerations for packet systems broadcast packet techniques on cable ♦ KEY W0R9S ARPANET packet switching computer networks broadcast packet systems cost reliability throughput routing vihv • ' ■• it Security CIu -- iv t' or Second Semiannual Technical Report December 1973 nr the Project The Practical Impact of Recent Computer Advances on the Analysis and Design of Large Scale Networks Principal Investigator and Project Manager Howard Frank 516 671-9580 ARPA Order No 2286 Contractor Network Analysis Corporation Contract No DAHC15-73C-0135 Effective Date 13 October 1972 Expiration Date 12 October 1974 Sponsored by Advanced Research Projects Agency Department of Defense The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies either expressed or implied of the Advanced Research Projects Agency or the U S Government Ik •' i ■ P ■ £NI A Network Mtialysis Corporation SUMMARY Technical Problem Network Analysis Corporation's contract with the Advanced Research Projects Agency has the following objectives ■ To determine the most economical and reliable configurations to meet growth requirements in the ARPANET ■ To study the properties of packet switched computer communication networks ■ To develop techniques for the analysis and design of large scale networks ■ To determine the cost throughput reliability characteristics of large packetswitched networks for application to Defense Department computer communication requirements ■ To apply recent computer advances such as interactive display devices and distributed computing to the analysis and design of large scale networks General Methodology The approach to the solution of these problems has been the simultaneous ■ study of fundamental network analysis and design issues ■ development of efficient algorithms for large scale network analysis and design ■ development of an interactive distributed display and computational system to deal with large-scale problems ■ application of the new analysis and design tools to study cost and terformance tradeoffs for large systems Technical Results In this report the following major accomplishments are discussed ■ ARPANET designs with up to 57 nodes were derived ■ A study of the effect of point-to-point and broadcast satellite channels on ARPANET cost and throughput was ompleted in Precedinu page blank Network Analysis Corporation ■ The second phase cf study of terminal oriented network cost and performance was completed ■ A new large network design technique based on cut-saturation was developed and found to be more cost effective than the branch exchange techniques urrently in use ■ Investigations of large network routing schemes were continued including new routing methods fo both high bandwidth and for partitioned networks ■ A multiplexing experiment to obtain low cost leased line terminal access to ARPANfcT was successfully completed Four CRT terminals are now operating on a single 4800 BPS line into ARPANET TIP ■ The first phase of an interactive network data handling system has been completed for an IMLAC display editing system for large network graphics ■ The definition of a network analysis problem solving system was completed This includes system definitions for network data structure manipulation network algorithm programming and the first phase in the specification of a network programming language ■ The first phase of a detailed event oriented simulation model to develop flow control and routing algorithms was completed for the packet radio system ■ Major progress was made in the development of flow control acknowledgement schemes and routing techniques for packet radio ■ A combinatorial model to study properties of message flow in packet radio networks was developed and extensively exercised ■ A spread spectrum model to investigate properties of the packet radio channels was developed ■ A study of the combination of packet broadcast techniques and two way coaxial cable systems for use in local distribution in urban and suburban environments was completed Department of Defense Implications The Department of Defense has vital need for highly reliable and economical communications The results described in this reporting per'od reinforce conclusions of earlier periods about the validity of packet switching for massive DOD data communications problems A major portion of the cost of implementing this technology will occur in providing i«_cal access to the networks Hence the development of local and regional communication tech- Network Analysis Corporation niques must be given high priority In addition the initial results on the use of domestic satellites indicates that substantial savings can be accrued by «heir use in large scale for DOD data communications lmplic iions for Further Research Further research must continue to develop tools for the study of large network problems These tools must be used to investigate tradeoffs between terminal 2nd computer density traffic variations the eff-cts of improved local access scheme such as p cket radio the use of domestic satellites in broadcast mode fo ' backbone networks and the effect of link and computer hardware variations in reliability on overall network performance The potential of these networks to the DOD establishes a high priority for these studies r Network Analysis Corporation TABLE OF CONTENTS PART 1 NETWORK PROPERTSES CHAPTER PAGE 1 ARPANET Growth 1 1 2 The Impact of Satellite Channels on Network Cost and Performance Part 1 Satellite Links in ARPANET 2 1 1 2 3 A 5 6 2 1 2 2 2 9 2 10 2 16 2 35 3 Introduction Problem and Model Formulation Dflay Routing and Throughput Analysis Optimal Number and Location of Ground Stations ARPANET Design Using Satellite Links Conclusion and Future Research Terminal Oriented Network Cost and Performance Part 2 3 1 1 2 3 4 5 3 1 3 2 3 8 3 16 3 18 Introduction Problem Evolution Network Modeling for Terminal Access Current Designs—TIP Cost—Performance Tradeoffs Preceding page blank VII ■A ü äfe'äiA Network Analysis Corporation TABLE OF CONTENTS PART 2 NETWORK TECHNIQUES CHAPTER 4 PAGE A Cut Saturation Algorithm for Topological Design of Packet Switched Communication Networks Part 1 1 2 3 4 5 6 7 5 6 i i 7 8 Introduction Description of the Cut Saturation CS Method Cut Saturation Algorithm Implementation Other Design Considerations Computational Requirements for the Cut Saturation Design Comparison Between the CS Algorithm and Other Existing Methods Condition and Future Work 4 1 4 1 4 2 4 4 4 23 4 27 4 30 4 38 Cost Computation for New Line Tariffs and Services 5 1 1 2 3 4 5 1 5 2 5 4 Introduction New Line Tariffs and Their Impact Line Cost Models An Algorithm for Optimizing Domestic Satellite Communications Networks for Computer Communications Part 1 5 8 Routir % Considerations for Large Networks 6 1 1 2 3 4 5 6 1 6 3 6 4 6 8 6 15 Introduction Hierarchical Structures Deterministic Routing Poll ies Adaptive Routing Policies Cor ciusion and Future Research Routing Algor'chm« for High Bandwidth Traffic 7 1 1 2 3 4 5 7 1 7 1 7 2 7 3 7 9 Introduction Distributed and Centralized Routing Algorithms Source and Destination Routing Algorithms Computational Considerations Conclusion A System for Large Scale Network Computations Part 1 8 1 1 2 3 4 8 1 8 2 8 6 8 14 Introduction Hardware Resources for Network Computations Software for Large Scale Network Computations The Netv ork Editing Language VIII Network Analysis Corporation TABLE OF CONTENTS PART 3 PACKET RADIO CHAPTER 9 10 i 11 Packet Radio System—Network Considerations ml 12 9 1 1 Introduction 9 1 2 Network Overview 9 2 3 4 5 Network Nodes Terminals Repeaters Stations Network Links The Channel Network Topology Repeater and Station Location 9 12 9 15 9 18 Routing and Acknowledgement Scheme for the Packet Radio System 10 1 1 2 3 4 5 5 7 10 1 10 4 10 8 10 18 10 27 10 34 10 40 Introduction Possible Routing Techniques Acknowledgement Considerations A Directed Routing Procedure A Procedure for Repeater Labeling Some Simulation Results Appendix An Example of Repeater Labeling Combinatorial Models for Analysis nf Message Flow in Packer Radio Nets 1 2 3 4 5 6 7 8 9 10 11 12 13 y r PAGE Introduction The Basic Model Outline of Questions The Number of Messages Received at the Ground Station Message Distribution with Type 1 Slotting Message Distribution with Type 2 Slotting Survival of Messages Distribution of Arrivals and Receptions Computer Analysis With A Closed Boundary Dynamics of A Single Message On Route Systems With Retransmissions Messages Outward From the Origin Other Models Summary of Results of Theoretical Models 11 1 11 1 11 4 11 7 11 10 11 12 11 12 11 15 11 24 11 40 11 72 11 86 11 99 11 130 Time and Space Capture in Spread Spectrum Random Access 12 1 1 2 3 4 5 12 1 12 6 12 9 12 16 12 28 Introduction Model and Assumptions Preliminary Analysis A Simulation Approach Appendix Method of Simulation IX vidjtfe ife Network Analysis Corporation TABLE OF CONTENTS PART 3 PACKET RADIO CONTINUED CHAPTER 13 PAGE Packet Data Communications OR MATV and CATV Systems A Feasibility Study 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 14 Introduction The In-Building Problem A Typical MATV System A Typical CATV System Data Options on MATV and CATV Systems Function of Experimental Digital System Design System Constraints Components of Experimental Systems System Tests Conclusion Appendix A Calculation of Error Rates for CATV System Appendix B Maximum Number of Active Terminals Appendix C Formulas for Traffic in Links Appendix D Design of Boston System Appendix E Specifications for Filters and Data Augmentation Devices References 13 1 13 1 13 3 13 5 13 9 13 14 13 22 13 24 13 26 13 64 13 74 13 79 13 84 13 86 13 95 13 102 14 1 Network Analysis Corporation CHAPTER 1 ARPANET GROWTH During this reporting period a total of ten new nodes TIP and IMP sites were proposed for addition to the ARPANET If the locations of all network nodes are known in advance it is clearly most efficient to design the topological structure as a single global effort However in the ARPANET as in most actual networks node locations are added and modified on numerous occasions On each such occasion the topology could be completely reopt imized to determine a new set of link locations In practice however there is a long lead time between the ordering and the delivery of a link and major topological modifications cannot be made without substantial difficulty It is therefore prudent to add or delete nodes with as little disturbance as possible to the basic network structure consistent with overall economic operation Figures 1 2 3 4 and 5 show the present and proposed ARPANET'S derived using a mixed policy of minimum incremental cost and disturbance to th network Figure 1 represents the present net while Figure 2 includes those TIP'S and IMP'S under immediate consideration or already committed for connection to the ARPANET Figure 3 contains in addition all the TIP's and IMP's that are still under active consideration Figure 4 consists of additional nodes that have been proposed but are not under active consideration Figure 5 contains nodes identical to those in Figure 4 but shows in addition the several suggested additional lines that would be required for additional reliability if ehe Figure 4 nodes were to be connected to the ARPANET Estimated line and modem costs and throughputs for the ARPANET at various stages of growth are given in Table 1 The costs and throughputs corresponding 1 1 Network Analysis Corporation to Figures 1 2 3 4 and 5 are given vespectively in the last five lines of Table 1 Locations of the IMP's and TIP's are given in Tables 2 a 2 b 2 c and 2 d 1 2 FIGURE 1 AS of December IJBL UTAH II F'Irfl n_ I LL IPPV NCC TIP HAWAII ANTS TIP TANFORD 1 3 ND UCSE A DC UCLA 5 etworlz Analysis Corporation Network Analysis Corporation o 4- u Ü 0 u u 0 T3 f—I E C r c ■-- ■ I fl V ' i o u c X a r '- ■' c c is ' '■u j C h- L U •f-t C V f a e- - u - o c x k 1 c 4J r H _ J nJ -P •H LI fc g r E F ' I-' ■■■ • 4 ■ „■ 0 r J Ö u U 2 r -i U r i 0 t O ■'' 4 • f' OJ Ü' -r- TS 3 c 3 •- a c r ij r-H u c 32 1 4 i J a u i •n -r •P u r 4J rX B XI 4-' 4J k u 4-' 4-' ■ti H Network Analysis Corporation r o •H 4- u c o ■H Jj l OJ c c c ü Q C C o o u c 14- o 3 1-1 0 V e D U C a c o ■H 4-1 d M OJ 'O ►J IX b 4-i «c C1 E •r-1 x 1-1 E- u-i o O 3 0 u r c K J O H u cn c u o K 0 x o c o ■H -1 3 M 4- ■r4 u X r bi U c f et c 3 •- U C 0 0 X U 4J 0 •H UJ 4- u 0 4- 0 ■r- •H 4-1 u 'V £ IT Di C •H o 0 D o c r r iH U 3 C 3 U i •3 in n cn •H ■•- -rH 4-» 4-1 4J a « It x x x « W 4- 4- 4- c U 0 0 0 4-1 -i-l 4-1 -H 4-1 -i-l WWW oHlS £ 1 5 ■ Network Analysis Corporation c 0 ■H 4J U ü c c c u X 00 u rn ro r- • 0 X £1 0 0 0 ■ •-• t -1 ji i o £_ M U U-' t 0 2 M 3 — — C w M Li- 'c a CJ in 0 E' a c r a 3 u x 3 •0 o J ' Jl rO r c •H •H T3 Q 4- 5 1t ' •H j M J2 V Z f u c ■H 0 o s tc 3 - 00 D u Q CO 1 6 u Ü ■l-l r ■l- 1 4-' t tZ i- u n o c '■ —i c c r u C 0 •r u 0 0 r— 4- 3 14 4J tu T3 0 c 0 •H t k-i c c ■H 0 4-1 V C O U 3 X 0 'O ■H 4J 0 o ■- X 1 •U 0 C in O X X 3 cd A3 U 0 TS X 3 X ö CT - Cn t-H c r Ci r-l ■H 0 ü f ' X X •M- Q C c 0 0 u c c H ' 4' -a u r L o w D cr 4- »4-1 _ ■p- 0 0 ■H IM c 7 B X K S-i r- 0 c 4J _ x c ' c - r 1 u to - 1 3 U e u m 0 M JJ 0 c 3 c tu 0 X ifl -H ■r- •H -p 10 jj 4J H c' 0 J5 X X _ r 4 ' X c ft c c D ü 4J •H 4J •i-J 4J •H 4J •H 00 K 00 00 Network Analysis Corporation 0 ■H 4J o cu c c 0 0 w u 4 0 u ' c ■ r •r-l • £ 4 0 4 • 4 1 U C ' eC V c Q i l » u V - 3-■« 41 L 0 U r- 14 li •-» X L t J K •H i— U» ►—' »-- u •r 10 j C4 C i' Q u 0 Cfl fl p P 4 4J u Q ü c • - t 0 4 ra c r •ü 4 r- c f 0 J -r- f 4 c c -' -rl r x p £ ■H 4 0 4 'S rH 4 0 H % 1 7 -4 U 0 4 U w c 4J r_ 3 X JJ 4 3 0 c iZ 0 j -i » - •— P V C1 r l c c u u 3 s r Ü ■a in 0 0 Ü 4 a - f- c 3 -4 tn tf 3 ■H ■H u •■'' 0 J W H-1 ■H •f c u •»- 3 o u r-i e •r- -r-i D u c c 0 £ £ C 4 3 K ■r 4 a fl --ff r'O a » X J c xs kH a 0 ü ■H ff Ü '1 0 CP 11 0 -r-i C- 0i JJ ■H — ' dl Z J G 4 Cu r c C- •r r a - 4 'U u £ 6 •i H- u 0 J ' o ■M H J r E- Ü t 4 r C t -•• t CV•' c 41 un l ■51 a F- 0 r £Ä r-l 4- i Cn C ■ i t rfl j- ■ QJ J ■r-i •r 13 D m Network' Analysis Corporation TABLE 1 ARPANET LINE COSTS AND THROUGHPUT Number of Nodes Yearly Line Cost K$ Throughput Uniform Traffic K Packet M Packet KBPS Node Day Node Day Line Cost Node K$ Line Cost K Packet cents 14 605 12 2 1690 23 66 43 2 7 15 659 12 5 1730 25 95 43 9 7 18 792 14 2 1970 35 46 44 0 6 21 825 12 4 1710 35 91 39 3 6 23 849 11 9 1640 37 72 36 9 6 24 860 11 1 1530 36 72 35 8 6 26 810 11 6 1600 41 60 31 2 5 30 859 10 1 1400 42 00 28 6 6 33 886 9 3 1290 42 57 26 8 6 39 1 016 8 7 1210 47 19 26 1 5 40 1 022 8 5 11G0 47 20 25 6 41 1 052 8 1 1130 46 33 25 6 6 4o 1 140 7 3 1010 46 46 24 8 6 50 1 189 6 4 890 44 50 23 8 6 57 63 lines 1 288 5 2 720 41 04 22 6 6 57 66 lines 1 343 5 5 760 43 32 23 6 6 Based on 24 hr day operation 1 8 Network Analysis Corporation TABLE 2 a LIST OF EXISTING TIP'S AND IMP'S Abbreviation on Map ABER AMES IMP AMES TIP ARPA Center Aberdeen Proving Ground N A S A Ames Research Center N A S A Ames Research Center NCC BELV Advanced Research Project Agency Bolt Beranek and Newmann Network Control Center BBN Fort Belvoir CASE CCA Case Western Reserve Computer Corporation of America CMU ETAC Carnegie-Mellon University Environmental Technical Applications Center Fleet Numerical Weather Control Air Force Global Weather Central Harvard University University of Illinois Information Sciences Institute MIT Lincoln Laboratories BBN FNWC AFGWC HARV ILL ISI LL MIT1 MIT2 MITRE NBS RADC RAND SDAC SDC SRI STANFORD MAL Project Mass Institute of Technology Information Processing Center Mass Institute of Technology MITRE Corporation National Bureau of Standards Rome Air Development Center Location Maryland Sunnyvale Sunnyvale Arlington Cambridge Cambridge Virginia Calif Calif Va Mass Mass Cleveland Ohio Cambridge Mass Pittsburgh Pa Washington D C Monterey Calif Offu tt A F B Neb Cambridge Mass Urbana 111 Los Angeles Calif Cambridge Mass Cambridge Mass Cambridge Mass Rand Corporation Seismic Data Analysis Center System Development Ccrporation Stanford Research Institute McLean Va Washington D C Rome N Y Santa Monica Calif Alexandria Va Santa Monica Calif Menlo Par1 Calif Stanford University Stanford Calif 1 9 Network Analysis Corporation TABLE 2 a Abbreviation on Map conf d Center Location UCLA University of California Los Angeles Los Angeles Calif UCSB University of California Santa Barbara University of California San Diego University of Southern Calif University of Utah Xerox Palo Alto Research Center Dept of Commerce Boulder Santa Barbara Calif UCSD USC UTAH XPARC DOCB TYMSHARE MOFFETT RML LLL L3L RU AFARL NOSAR HAWAII UL Tymshare Inc Moffett Field Range Measurement Lab Lawrence Livemore Lab Lawrence Berkeley Lab Rutgers University Air Force Aeronautic Research Lab Norway Seismic Array University of Hawaii University of London 1 10 ■ ■ San Diego Calif Los Angeles Calif Salt Lake City Utah Palo Alto Calif Boulder Colo Cupertino Calif Sunnyvale Calif Patrick AFB Fla Livemore Calif Berkeley Calif New Brunswick N J Dayton Ohio Kjellas - Norway Hawaii London England Network Analysis Corporation TABLE 2 bl TIP'S UNDER IMMEDIATE CONSIDERATION Abbreviation on Map Center AFWL SMC PURDUE AFADC EDAM SIMP Location A F Weapons Lab Stanford Medical Center Purdue university A F Armament Development Center Albuquerque N M Stanford Calif Lafayette Ind Fort Walton Fla COMSAT Edam W Virginia TABLE 2 c TIP'S STILL UNDER ACTIVE CONSIDERATION Abbreviation en Map NYU NSA GAFB ARPA2 Center New York University National Security Agency Günther Air Force Base Advanced Research Project Agency Second TIP Location New York City N Y Fort Meade Maryland Montgomery Alabama Arlington Va 1 11 ■' ■ ■ •j j £ h ' -u j Network Analysis Corporation TABLE 2 d SITES HAVING BEEN PROPOSED BUT NOT UNDER ACTIVE CONSIDERATION Abbreviation on Map Center USAWC U S Army Weapons Command USAAC ANL U S Army Aviation Command Argonne National Lab AEDC HANSCOM LOS AL Arnold Engineering Development Center Hanscom Field Los Alamos National Lab 1 12 ■ -■ i Location Rock Island 111 St Louis Mo Argonne 111 Tullahoma Tenn Kanscomfield Mass Los Alamos N M Network Analysis Corporation CHAPTER 2 THE IMPACT OF SATELLITE CHANNELS ON NETWORK COST AND PERFORMANCE Part 1 Satellite Links in ARPANET 1 INTRODUCTION This chapte contains the preliminary results of a costthroughput study considering satellite links in ARPANET Satellite bandwidth is leased from a common carrier and satellite access is possible only through carrier's ground stations Two schemes for satellite access are considered A Point-to-Point connections consisting of full duplex channels between pa rs of IMPs say A and B consisting of terrestrial connection from A to the ground station nearest to A from B to the ground station nearest to B and a satellite hop between the two ground stations With the exceptioi of cost and delay characteristics this link can be modeled as a normal terrestrial link for routing and throughput computations B ALOHA multiple access connection SIMPs satellite IMPs are connected to the ground stations and to one or more network IMPs Packets arriving at a SIMP from terrestrial links are transmitted on the satellite channel either in specific time slots slotted ALOHA or as soon as they reach the head of the SIMP transmitting queue unslotted ALOHA If two stations transmit simultaneously the two packets interfere with each other and must be retransmitted To compute delay routing and throughput a special model of the ALOHA channel is developed in Section 4 1 '■I Several alternatives for ground station selection ■' satellite access implementation are considered for the present ARPANET and the results are compared 2 1 '■mmmmm Network Analysis Corporation Although the emphasis in this report is in the area of ARPANET applications the development of simple general network models for satellite channels and an exact solution of the ground station location problem in an idealized geometry is also considered Future studies will extend this work into the area of v ry large networks and less idealized models 2 PROBLEM AND MODEL FORMULATION Two new variables ground station location and satellite access scheme must be considered when satellites are added to conventional terrestrial networks The general design problem can then be formulated The design problem is aimed at finding a minimum cost configuration including a terrestrial network design ground station locations with an appropriate access technique and network routing sc _hat time delay and reliability constraints are satisfied 2 1 SATELLITE FACILITIES COST AND CHARACTERISTICS The satellite facilities considered here include satellite channel ground station SIMP and line connections from SIMP to station or from IMP to station The following costs are assumed A Satellite Segment Bandwidth Kbs Cost $ mo 100 50 full duplex 460 230 full duplex 1 500 B 2 500 5 500 8 000 Local Loop Station to SIMP or station to central office Bandwidth Kbs Cost $ mo 50 full duplex 230 full duplex 1 000 1 300 2 2 ■ ■ ■ 1 r ■ Network Analysis Corporation To connect an IMP to a ground station IMP to central office and central office to station connections must be purchased C SIMP Two types of SIMPs are assumed regular bandwidth greater than 1 500 kbs and cost - 5 500 SIMP corresponds to the high speed version of IMP development of BBN It can support a combination SIMP with $ mo This presently under of land traffic rates L and satellite traffic rate S such that L 3S 1 500 D A small SIMP with bandwidth 600 kbs and cost 1 400 $ mo which is structurally similar to the H-316 IMP and is presently being developed by BBN The throughput equation is L 3S 600 2 2 SATELLITE ACCESS TECHNIQUES Packet delay on the satellite channel utilization and optimal packet routing depend on the access technique us d Point to Point access divides satellite channel bandwidth into subchannels each corresponding to a full duplex point to point connection between two given ground stations Multiple access allows any station to communicate with all other stations using the satellite down link in a broadcast mode transmitting simultaneously to all stations The multiple access techniques are divided into channel division techniques where the channel is divided into frequency e g FDMA or time e g TDMA frames and each irame is preassigned to a given ground station for transmission to the satellite and channel contention techniques where 2 3 f ■ wm tm tem Network Analysis Corporation each ground station can compete for use of the total channel for transmission to the satellite e g random access ALOHA schemes reservation schemes etc It is also possible to implement hybrid access techniques with one portion of the channel dedicated to point to point requirements and the remaining portion used in a multiple access mode 2 3 CHANNEL MODELS Assume that packets arrive at the ground stations in a Poisson fashion and that packet length is exponentially distributed The average packet delay for both point to point and multiple access channel division cases has the same expression as the delay for terrestrial channels In particular T l —— uC 1 u p l-f C s where T delay on i th channel sec C capacity of i subchannel bits sec f rate bits sec on i th subchannel i average packet length bits P satellite propagation delay - 27 sec The multiple access channel contention case is more difficult to analyze because of the possibility of interference from packets transmitted by different ground stations Here consideration is 2 4 Network Analysis Corporation limited to the ALOHA case The following assumptions are made 1 The number of ground stations is very large this leads to a worst case condition 2 Packets are of constant length equal to block size 3 Packet arrivals are Poisson distributed and 4 If collision occurs a packet is retransmitted after a random interval uniformly distributed between zero and k seconds Under these assumptions the average packet delay T the sum of propagation and retransmission delays is given in the case of unslotted ALOHA channel by ♦M fc - T Pg P_ S» - „ - l 2 where e — 2G G f C probability of non collision between two packets f C global channel utilization global satellite traffic including retransmission satellite channel bandwidth Since S Ge_2G 3 where S f s C effective channel utilization effective satellite traffic not including retrans- f missions T is uniquely determined given S 2 5 t ■ Network Analysis Corporation The maximum channel utilization obtainable with unslotted ALOHA is l 2e 184 An exact closed form expression of T S is not possible Therefore a convenient analytical approximation is desirable Assuming that k P T - Ps e 4 Consider the following approximation T S to eq 4 Ta S - Ps 1 - f j-i 5 It can be easily verified that T o T a o T' o T' o a For S 11 we have T ll 1 35 P s T a 11 1 55 P s This approximation was found to be sufficiently accurate for the purposes of ehe present study Notice that Equation 5 can be rewritten as fc lows Ta S - p 1 - i - 1 6 s where c C -jT effective unslotted ALOHA bandwidth If eq 6 is compared with eq 1 it is found that the unslotted ALOHA channel delay can be approximated by the delay of a M M l channel with bandwidth C' using proper packet length and propagation time A similar analysis is possible for the slotted ALOHA channel The delay T is T a ps 1 i T T TTC 2 6 7 Network Analysis Corporation where C C e effective slotted ALOHA bandwidth 2 4 NETWORK MODELS As an example of the issues that must be handled to construct satellite network models under different access techniques suppose a system contains four ground stations There are several possible cases A Point to Point Access Suppose the total bandwidth C is divided into four full duplex point to point channels A-B A-D OB C-D Then the equivalent network is represented in Figure 1 where each link has capacity C C 8 Link delays are as in eq FIGURE 1 Point to Point 2 7 1 Network Analysis Corporation B Multiple Access Channel Division The equivalent model is shown in Figure 2 where the satellite is represented as a store and forward node Up-link channels have capacity C 4 and delay as in eq 1 down-link channels have infinite cap 'ity and zero delay C- C 4 for up-link C FIGURE 2 ' for down-link Multiple Access Channel Division C Multiple Access ALOHA The equivalent model is shown in Figure satellite is represented by two store and forward valent channel between the tw podes has capacity C 2e for unslotted ALOHA ana C C e for slotted 2 8 3 where the nodes The equiC where C ALOHA and delay Network Analysis Corporation given by eq 6 or 7 All ether links have infinite capacity and zero delay To compute average dslay optimal routing policy and throughput of a mixed terrestrial and satellite network we replace the satellite links with the appropriate equivalent network and use traditional queueing formulae and routing algorithms °° V i except for C FIGURE 3 ALOHA Access 3 DELAY ROUTING AND THROUGHPUT ANALYSIS Traditional ARPANET design requires an average delay T 200 sec If the same requirement was to be maintained after introduction of satellite links then satellite utilization would be very small 2 9 Network Analysis Corporation since satellite propagation delay alone is equal to 270 sec Thus the problem should be approached by considering two classes of traffic interactive and background The 200 sec requirement is then applicable to the first class while larger delays are allowed for the second one In this preliminary phase of research the following simple approach is used Initially it is assumed that there is only one class of traffic The delay on a satellite link is assumed to be given by where C is a proper value of capacity dependent on the access scheme The optimal routing problem under this assumption is used to find the maximum throughput that can be accommodated with an average delay 200 sec Finally the amount of traffic that uses the satellite is computed and the actual satellite delay using the exact delay expressions is calculated The final solution contains two components of traffic terrestrial traffic with average delay equal to 200 sec and satellite traffie with average delay equal to 200 sec satellite delay 4 OPTIMAL NUMBER AND LOCATION OF GROUND STATIONS 4 1 GENERAL The global satellite network design requires the selection of ground station numbers and locations The optimal location problem is a difficult integer type problem and no efficient general so LUtion methods are currently available However in most practical applications there are a limited number of locations at which ground stations exist or can be installed In such cases the location problem is efficiently solved by analyzing and comparing only a few reasonable alternatives 2-10 Network Analysis Corporation In this section - we establish a generalized relationship between the optimal number of ground stations and other important design parameters such as cost and throughput In addition the impact of the access scheme on total cost and number of stations is evaluated To carry out the analysis a simple terrestrial network geometry is considered in which the nodes are uniformly distributed along a circle and are connected in a loop with ground stations symmetrically located on the circle Traffic requirements are spanned uniformly between all node pairs Multiple access schemes are allowed as well as a point to point access scheme in which diametrically opposite ground stations are connected by point to point satellite links Traffic requirements between any two node pairs can either be accommodated along the terrestrial loop network or can be routed to the nearest grouud station and then transmitted over the satellite channel This routing decision affects the total communications cost since terrestrial and satellite links must be sized according to link traffic rate In this study the following assumptions are made link capacities are continuous variables and any value of capacity can be purchased The incremental cost of link capacity is constant for a given link Thus cost is a linear function of capacity Finally for each link an amount of capacity equal to the average link traffic rate is purchased i e queueing delay is disregarded Using the above assumptions it can be shown that the optimal routes are the shortest ones computed according to incremental link costs 4 2 PROBLEM FORMULATION The ground station location problem is formulated as follows Given network geometry traffic requirements type of satellite access 2 11 - ■ i K--- w« -t '- vv- v - Network Analysis Corporation Minimize 'over number of stations and routing total communications cost Such fiat traffic requirements are satisfied To solve the location problem the number m of ground stations is first assumed to be given Therefore ground station locations ate given by symmetry considerations The minimum cost routing problem for the associated network configuration is then solved Using reasonable approximations a closed form solution for the minimum cost D m in terms of m is obtained Next the optimal value of m with a one-dimensional optimization on D m is calculated The following notation is used NN Number of nodes r Radius of the circle on which nodes are located miles m Number of ground stations DG Monthly cost of the ground station including the cost of the connection into the terrestrial network as well as the cost of the station and a function of the access scheme used d Monthly cost of satellite bandwidth $ Kbs x month d„ Monthly cost of terrestrial bandwidth $ Kbs x mile x month S d yd» s Equivalent terrestrial length of the satellite link miles A 2 12 Network Analysis Corporation R Traffic requirement Kbs node pair The results for the point to point and multiple access schemes are presented in the next sections FIGURE 4 Point to Point Access 4 3 POINT TO POINT ACCESS To obtain a simple analytical treatment when studying point to point satellite configurations it is assumed that point to point links are established only between diametrically opposite ground stations See Figure 4 Clearly more complex point to point configurations can be proposed which would require a separate analysis for each case J 2 13 W„ - -Ä-Vvfe 4A Network Analysis Corporation The following expressions of minimum cost D corresponding to the minimum cost routing strategy then apply - case of m o no ground stations Dt NN2 R dz -y r 1 - case of m 2 NN2 R dQ g Dfc 2DGS 3Tir 2S 2 r 1 s s 2-s 3 - case of m 2 NN2 R dz D t GS 4 - optimal value of m for m 2 I m - 2 R d„ Trr - s NN £ 4 GS Notice from Equation 3 that the bandwidth cost given by D t - mD « decreases with m until it reaches the JO 2 lower bound NN R d» frr 4 S 2 for m -»■ °° If S o i e satellite bandwidth has zero cost the lower bound is exactly one half the cost without satellites See Eq 1 Equation 4 shows that m critically depends on throughput 2 NN R on DGq» and on region size r it does not critically depend on S Recall that typically s r 4 4 MULTIPLE ACCESS Only the case m 3 is considered because m 2 can be better implemented with a point to point connection when requirements are assumed uniform Then 2 14 Network Analysis Corporation n „D„ t VJO -V m - NN s 1 « ¥ i - NH2 R ' 5 I« - Al I 5 R d£ 2irr -j 2D « S 5 6 Notice from Equation 5 that the bandwidth cost D - mDcs decreases with m more rapidly than the corresponding cost of the point to point case and becomes only satellite bandwidth cost for m -»• °° The optimal number of stations m displays the same behavior as in the point to point case 4 5 EXAMPLE Let 7 000 $ month for multiple access D GS i 1 300 $ month for point to point NN2 R d 500 Kbs 13 $ mile x Kbs 5 5 $ Kbs s 40 miles r 500 miles d s The optimal number of ground stations using point to point links is PP m J 500 x 13 x 1500 V 4 x 1300 _ v 4 3 ' - 4 2 15 Network Analysis Corporation Using multiple access ma V f 500 x 13 x 3000 2 x 7000 3 7 The corresponding minimum costs are 1 Point to Point cost DJ t pp 5 200 30 000 35 200 Ground Bandwidth Station 2 Multiple Access cost D x ma 28 GC3 24 000 52 000 Giound Station Bandwidth For this particular application inspite of the fact that the multiple access scheme provides a much lower oandwidth cost the point to point access ij more economical because of the higher cost of multiple access ground stations 5 ARPANET DESIGN USING SATELLITE LINKS 5 1 ALTERNATIVES FOR SATELLITE ACCESS IMPLEMENTATION In this section cost-throughput trade-offs for various satellite access schemes in a recent 43 node ARPANET configuration See Figure 5 are evaluated In particular the following types of implementation are considered A No satellite links The capacity of the 43-node network is upgraded by introducing terrestrial links only Cost and throughput trends re compared to those of the satellite case 2 16 ' ii Mi ' r -' -- - -1 ''-- '■• ''''w Network Analysis Corporation B Three ground stations in San Francisco Los Angeles and Washington D C are available for satellite access Various configurations with two or three stations and with multiple or point to point access are considered For the terrestrial configuration two cases are considered 1 terrestrial network unaltered and 2 terrestrial network reoptimi2ed C Five ground stations in San Francisco Los Angeles Washington D C New York and Chicago are available for satellite access In addition to the alternatives studied for the three ground station case capacity reductions of terrestrial links from 50 Kbs to 19 2 and 9 6 Kbs are also allowed These reductions are made possible by the larger number of stations available A hybrid implementation which includes both multiple and point to point access is also analyzed For each satellite alternative a network optimization is carried out by first selecting satellite stations from the set of available locations Ground station to network connections and in the case of point to point access satellite links are then assigned in this step the terrestrial network topology is optimized to achieve the best cost-throughput tradeoff 5 2 RESULTS Computed for each network configuration is total cost terrestrial cost of all terrestrial links satellite cost cost of GIMP if applicable connection from SIMP to station or from IMP to station and satellite bandwidth total throughput traffic on satellite and satellite channel delay i i 2 17 Nt twork Analysis Corporation A No Satellite Links TOTAL COST K $ mo NETWORK CONFIGURATION Present 43 node configuration Figure 5 93 Upgraded 43 112 9 node configuration Figure 6 B TERR COST K S mo SAT COST K $ mo THRUPUT kbs 93 — 447 112 9 -- 635 SAT TRAFFIC kb SAT DELAY sec Three Ground Stations Available 1 Unslotted ALOHA unaltered terrestrial topology 3 Regular SIMP'S 113 300 Figure 7 99 29 3 670 214 2 Regular SIMP'S 122 300 at Los Angeles and Wash D C Figure 8 100 22 3 670 212 16 3 641 175 3 Small SIMP'S Figure 9 2 115 500 2 Point to Point Links Figure 1 4 Unslotted ALOHA optimized terrestrial topology 2 Regular SIMPs 113 300 at Los Angeles and Wash D C Figure 10 3 99 2 4 91 22 3 618 212 4 Point to Point Access unaltered terrestrial topology 109 500 93 16 5 2 18 661 212 27 4 Point to Point Accesr optimized terrestrial topology TOTAL COST K $ mo TERR COST K $ mo 101 6 1 Point to Point Link of 230 kbs Figure 13 1 Point to Point Link of 50 kbs Figure 14 NETWORK CONFIGURATION 2 Point to Point Links Figure 12 SAT COST K $ mo THRUPUT kbs SAT TRAFFIC kbs SAT DELAY sec 85 1 16 5 745 320 27 95 8 85 1 10 7 672 270 27 91 3 85 1 6 2 347 92 27 Five Ground Stations Available 1 2 Point to Point Links Figure 15 2 Point to Point Access optimized terrestrial topology 91 9 75 16 9 654 330 27 Slotted ALOHA Access optimized terrestrial topology 3 Regular SIMPs 108 3 at San Francisco Chicago Wash D C Figure 16 79 29 3 686 393 5 Small SIMP'S Figure 17 75 9 21 8 603 353 97 7 5 3 Hybrid Access unslotted ALOHA 2 point to point links optimized terrestrial topology Hybrid configuration Figure 18 101-7 75 9 2 19 25 8 584 330 4 Network Analysis Corporation o OS CC c in U OS a EH »— O M »- -« o u w 2 0 OS u en Hi OS 0 2 20 Analysis Corporation 1- UP 3RD 7 Network Analysis Corporution 22 3 N'c tunrlc Corporahon AF - 23 2 24 - SIHP FIGURE 9 3 SVALL SIMP uv- r'vi 25 11 2 ETCURE 10 Network Analysis Corpora on 26 - r 2 POINT EQURE Ll TO UNA TOPOID Artwork Ana 1 sis Corporation 230 2 27 50 33-6 2 FIGURP Lg TO POINT f I rn TOPOLOGY erwurk Analrsis Network Analysis Corporation C O iJ c c oiQ ' - O K • -■ S ' ü H I S H a i- — H C o EH O 2 28 POINT T0 LINK all udk - - 31 - 0 1 JAIIULI Jam- 3 30 Newark Analym ration bs a Oi 31 _f G 8mm mtg O 'fhd 3 17 M-m ork Analysis Carporanon WHOM i 4 10 g HLOJ IIHHAH 8 33 5 3 DISCUSSION A general comment valid for all the satellite configurations considered is that satellite links are economical for throughput levels which are about 50% higher than the maximum throughput accommodated by the present terrestrial ARPANET configuration However changes in network topology and the reduction of some link capacities to 19 2 Kbps and 9 6 Kbps are required to take advantage of the economies available The fact that satellite links become attractive only for a relatively high throughput level is due to the high cost of network to ground station connections However many other factors disregarded in this preliminary analysis must be taken into consideration before general cost-performance trends are evident In particular the evaluation of point to point satellite link cost assumed that the standard IMP softv re can support satellite rates up to 230 Kbs There are indications however that such a high rate will require modifications of the IMP hardware and software and therefore will raise the cost of point to point links to the same levels as those of multiple access As for satellite bandwidth efficiency it must be mentioned that with additional software cost reservation techniques for multiple access can be implemented on the SIMP and such techniques can theoretically increase effective satellite bandwidth up to capacity Furthermore multiple access allocates satellite bandwidth dynamically according to traffic pattern changes and if needed allows any two stations to use the full channel while point to point access corresponds to a rigid bandwidth allocation between pairs of stations Considering the solutions obtained using five ground stations case c yield that performance is considerably better than with on y three stations available This is mainly due to the presence of a ground station in Chicago which allows reduction of channel 2 34 capacity on the cross country connections Satellite traffic on the other hand is much higher in this case Therefore if we assume that the maximum available satellite bandwidth is 1 5 Mhz we must use the slotted ALOHA access which provides better bandwidth utilization but requires synchronization techniques Cost and throughput performance for the hybrid configuration are only slightly inferior to that of the slotted ALOHA case see C 3 However the hybrid configuration uses an unslotted ALOHA scheme for the multiple access portion of the bandwidth and therefore is simpler to implement than the slotted ALOHA scheme Satellite delays never exceed 5 sec Therefore the total average delay averaged over satellite and terrestrial traffic is always less than 5 sec The comparison of cost-throughput trends between implementations with and without satellite when network throughput is increased shows that satellite implementations can provide higher throughput at a lower cost especially if the terrestrial network is reoptimized 6 CONCLUSION AND FUTURE PESEARCH The results of the present study show that satellite links can offer substantial savings to ARPANET growth and can maintain average packet delay within acceptable limits Therefore they should be included in ARPANET short and long range plans Further research is required in the following areas 1 Careful comparison of various access techniques in particular point to point and multiple access using more accurate data for equipment cost and characteristics 2 Development of optimal deterministic and adaptive routing techniques for two classes of traffic interactive and batch in the presence of satellite channels 2 35 3 Study of the impact of type of satellite access on network reliability 4 Study of the impact of satellite technology on large networks i e satellite links in the highest hxerarchical level delay routing reliability implications etc 5 Study of flow control schemes to prevent congestion and therefore very high delay on the ALOHA channel 2 36 CHAPTER 3 Network Analysis Corporation TERMINAL ORIENTED NETWORK COST AND PERFORMANCE-PART 2 1 INTRODUCTION The interconnection of different time-sharing computers through a sophisticated communications subnet in the ARPANET gives terminal users access tc a variety of time-sharing resources Initially ARPANET development was directed toward computer-computer communications and user protocols Originally only terminals connected directly to a computer in the network had access to the network The successful completion of this initial phase led to a desire to complement resource development with increased user access Many Terminal Interface Processors TIP's have already been installed and are currently in use connecting users with a terminal but with no local Host computer to the network Complimentary to the TIP has been the development of the ARPA Network Terminal System ANTS a terminal-access port designed to provide greater terminal variability and a degree of on-site processing for terminal users The success of these developments and the present interest in continued development indicate a strong future for terminal access expansion The use of the ARPANET approach within the Defense Department would involve hundreds of Hosts accessed bj tens of thousands of low speed terminals Effective economical terminal access to the ARPANET and to similar networks will depend on continued development of such facilities as TIP's and ANTS's as well as on complimentary development of techniques for cost-effective utilization of these facilities This chapter continues the study of this problem There are several ways to provide terminal access into the network In particular multidrop lines for connecting terminals to access ports and packet radio techniques provide potential low cost network access methods It is necessary to investigate both of these schemes to evaluate the merits of each and to determine the conditions under which either may be preferable It is not unreasonable tc anticipate that both approaches may be applicable 3 1 - - Network Analysis Corporation within the same network In Part 1 of Semiannual Report #1 an effective algorithm was described for the multidrop line-layout problem The cost-effectiveness of the network design will depend not only on the line layout but also on the number location and characteristics of the ports into the network In this chapter we provide the foundation for the investigation development and evaluation of design tools for the effective and efficient placement of ports for terminal access Presently efforts have been directed toward 1 developing a model for use in terminal access design procedures and 2 estimating the cost of terminal access as a function of the number of terminals and traffic using existing design techniques The models developed for use in terminal access design procedures will serve as a basis for estimating terminal access costs as a function of the number of terminals traffic and the particular design The models are currently being used to estimate the cost of connecting terminals to the network through the use of TIP'S and multidrop lines The estimates cover a wide range of terminal numbers and traffic conditions and are developed with the use of the previously reported multidrop line-layout algorithm and engineering judgement selection of TIP locations These estimates will serve as a basis for comparison with other access approaches and as a measure of the effectiveness of new design tools 2 PROBLEM EVOLUTION The original ARPANET architecture was based on a sophisticated communications subnet composed of Interface Message Processors IMP's interconnected with 50 KBS lines Each IMP served up to four Host computers each of which was connected to its own set of terminals as shown in Figure 1 a The Terminal Interface Processor TIP is a modified version of the IMP with extended hardware 3 2 Network Analysis Corporation 52 FIGURE 1 ARCHITECTURES Network Analysis Corporation and software This Terminal IMP or TIP serves in the communication subnet and has the ability to serve a Host computer in the same manner as an IMP but differs from an IMP in that it also has the ability to connect directly with up to 63 terminals It creates a a form of network architecture as shown in Figure 1 b Although the TIP provides a means of direct access to the network by terminals it does not provide local processing capabilities to terminals To fill the gap between an IMP-Host combination and the direct access TIP a mini Host computer system was developed This system the ARPA Network Terminal System ANTS provides a limited amount of on-site processing power and provides for a greater range of terminal variability The ANTS is based on a PDP-11 minicomputer system which acts as a Host to interconnected IMP's or TIP's Terminals are then connected to the PDP-11 which provides no resource to the network but permits access by the terminals The ANTS is a third variation of network architecture as shown in Figure 1 c ANTS's and TIP's are the two types of terminal access ports currently used in the ARPANET each of which must also serve as an ordinary message switching processor Thus such ports may be expected to be reasonably expensive and of high bandwidth To interconnect a large number of interactive terminal users to the network it is very attractive to consider such ports as the roots of centralized networks composed of multidrop facilities for which cost-effective multiplexing and concentration techniques may be applicable Suv-h a network architecture is shown in Figure 2 The actual port for network entry may be an extended version of the TIP a version of ANTS or some new development The design techniques developed in this study will only take into consideration the parameters characterizing the cost and constraints of the different facilities not the internal characteristics of the facility itself To estimate the cost of terminal access to the network it is assumed that continued development of terminal access ports will 3 4 Network Analysis Corparation 9W HOST IMP HOST FIGURE 1 b ARCHITECTURES 3 5 - nwow Network Analysis Corporation HOST IMP HOST dob ARPANET ARCHITECTURES IMP HOST FIGURE l C 3 6 ANTS 66b IMP IMP HOST 6 9 3 7 ANTS Network Attaiyu's Corporation permit the use of the multidrop line architecture described above Attention is therefore concentrated on the cost-performance aspects of this architecture and on the development of effective design techniques 3 NETWORK MODELING FOR TERMINAL ACCESS The process of investigating and developing approaches to the design of networks for terminal access requires as a first step the construction of an appropriate model In this study a primary goal is to determine the tradeoffs and parametric dependencies present in various app oachJS to terminal access To compare these approaches it is necessary to have a common data base to which each approach can be applied Such a base has been constructed in the form of a model for the number and geographic distribution of terminals for th° terminal and terminal user and for the multidrop communication lines It is also necessary to model those components of a design peculiar to the particular approach considered In this report we present a model for both the TIP system and the ANTS The following describes these various models 3 1 POPULATION The cost of terminal access will depend on a variety of factors including the number of terminals to be connected and their geographic distribution To determine the parametric dependence of cost on the number of terminals populations of from 100 to 10 010 terminals will be considered The figure of 100 reflects the anticipated near-future requests for terminals The figure of 10 000 reflects a realistic estimate of the number of terminals that can be expected to be served by a fully developed network The above consider only terminals without a local Host To have a meaningful data base it is necessary to geographically distribute the terminals in a sensible manner Terminals 3 8 Network Analysis Coiporation were located on the basis of population density because of the success of this approach in previous NAC investigations Figure 3 shows the placement of 1 000 terminals based on a distribution proportional to population A rectangular region was determined for each city or collection of cities to reflect the feasibility of the region to support a population segment with access to urban facilities Thus consideration was given to natural geographical boundaries such as mountains lakes and coast lines to major roads in the area to the number of nearby smaller communiti s and to the natural pattern of urbanization between relatively close major population centers Using this approach 12 3 regions were defined with varying sizes of approximately 70 miles square Once a number of terminals has been allocated to a region in proportion to population the geographic positions of the terminals within the region are uniformly randomly distributed With a large number of terminals it is reasonable to anticipate that some of them may be located at points with no discernible geographic significance Therefore a fraction a of the terminals were located at random in a large geographic segment east of Denver west of Pittsburgh north of Austin and south of Milwaukee The fraction a was selected on a sliding scale as shown below Number of Terminals In Regions 100 200 95% 95% 90% 90% 85% 500 1 000 2 000 5 000 10 000 80% 80% Random 5% 5% 10% 10% 15% 20% 20% Thus the data base developed will be used to evaluate various terminal access approaches and design procedures 3 9 cations of the 1000 node Numbers indicate multiplicity DE m de Nodes without numbers have multiplsemi f one simple nodes 3 Network Analysis Corporation 3 2 TERMINAL - TERMINAL USER Even though network resources in the ARPANET have been extended far iyond traditional time-sharing the interactive user retains a significant role in network usage and the extension of accessibility to a terminal basis will give even greater significance to terminal-computer traffic To effectively design and evaluate terminal access networks it is necessary to model the terminal traffic Two of the few definitive papers on time-sharing modeling from a communications perspective have been written by Jackson and Stubbs Jackson 1969 and Fuchs and Jackson Fuchs 1970 The following traffic characteristics of a terminal during a period of use are based on their results for time-sharing systems used in scientific applications and extended in consideration of advances in terminal technology higher speed lines being used and more sophisticated time-sharing users and programs Average Message Minimum Average Length User Input Computer Response 12 1 char 52 8 char Traffic 1 char sec 1 0 char sec Maximum Average Traffic 1 char sec 10 char sec The design of terminal accjss networks and hence the cost is anticipated to be dependent on the traffic level assumed for the terminals Thus in this study traffic level will be varied to investigate this dependence with a range of variation from the minimum to the maximum values indicated above The minimum average traffic level reflects the results of the noted study for scientific applications using low speed facilities and ordinary time-sharing programs The maximum average traffic level reflects an extension of these results in consideration of smart-fast terminals higher speed communication facilities more advanced time-sharing programs and more sophisticated users For comparison purposes all network designs will be based on busy hour conditions of all terminals being active 3 11 Network Analysis Corporation 3 3 COMMUNICATION FACILITIES The current ports for access by terminals to the ARPANET TIP's and ANTS's may connect terminals directly or remotely through modems and phone lines In this study a large number of terminals serving interactive users are considered and to economically connect all the terminals multidrop lines will be used The multidrop communications facility will be assumed to be a stcmdard voice-grade line as described below 3 3 1 MULTIDROP LINE Capacity full duplex 1200 bps Cost $ 50 mile $40 drop The cost is rased on the Government rate of $ 42 mile plus 20% for non-direct routing It should be noted that in this model the number of drops on a line is restricted only by the traffic constraint In reality the number is often additionally restricted by telephone company practices The effect of a more severe restriction is easily seen by simply assuming a correspondingly higher traffic level 3 3 2 TIP The first approach to be considered will be a TIP serving as the root of a centralized network of terminals In this section we note the significant features of the TIP In a later section we incorporate this description to construct a complete network model for design and cost evaluation The TIP as described by Ornstein et al Ornstein 1972 is characterized in Figure 4 Its characteristics indicate 1 The TIP has 63 terminal I O slots 2 Each slot can handle direct terminal connections or connections via modems 3 Asynchronous data rates handled by the TIP include 1200 1800 and 2400 bps 3 12 Traffic T 50KB Line MULTI-LINE h - 316 COMPUTER CONTROLLER CENTRAL LOGIC up to 63 IU IU n MODEM N -number of terminals ADEEM Ö FIGURE 4 TIP 3 13 Network Analysis Corporation 4 The TIP has a terminal program throughput of a 100 Kbps one way traffic if messages are long many characters and b 5-10 Kbps if each terminal message is a single character 5 The TIP uses 5% of its processing capacity to act as an IMP 6 The TIP uses 10% of its processing capacity to field MLC interrupts 7 The bandwidth capability of the TIP is summarized approximately by the formula P H 11T 850 where P total phone line traffic Kbps H T and full standard and full total Host traffic Kbps total terminal traffic Kbps duplex units count twice baud rate i e full duplex 50 Kbps phone line counts 100 duplex ASR - 33 counts as 220 As noted the TIP does not presently handle multidrop lines Consequently adjustments to its characteristics are required for the network model The above noted characteristics reflect TIP capacity as a message concentrator for terminals Additional consideration must be given to TIP cost which includes estimated rental rate the cost of its interconnect to the ARPANET and the cost of the modems necessary to connect terminals Therefore the total cost is a function of the TIP's geographical relationship to the rest of the ARPANET the topology of its interconnection and the number of modems required for terminal connections These costs will be determined as follows 50 Kbps line ARPANET interconnect $5 mile $425 end based on current ARPANET experience 3 14 Network Analysis Corporation 1200 bps line terminal connection $17 modem current standard cost TIP rental $2500 month assumed TIP cost of $100 000 to be amortized over 5 years at 10% interest compounded quarterly 3 3 3 ANTS The ARPA Network Terminal System ANTS provides a powerful access port for terminals Bouk 1973 The system is based on a PDP-11 minicomputer attached to an IMP or TIP The minicomputer acts as a full capacity Host for the IMP and offers terminals some local processing power The system has a higher degree of tailorability providing access and control to a wider range of terminals and peripheral hardware than the TIP Its incieased flexibility makes the ANTS more difficult to evaluate for terminal access and its cost effectiveness depends on the special terminals and local processing as well as on the number of ordinary interactive terminals connected to it At this point the ANTS will be considered strictly for terminal access and a system configuration oriented toward maximum terminal access bandwidth rather than local processing will be assumed Estimates of significant ANTS characteristics are 1 Terminal Bandwidth - 12 8 Kbps 2 Monthly rental - $l 000 month 3 1200 bps line terminal connection $17 modem If ANTS's are connected into the network at existing IMP's the only cost for the terminal port is the ANTS cost However the load of the ANTS on the IMP coupled with the existing Host computer must not exceed the capacity of the IMP If ANTS's are located at new points requiring their 3 15 Network Analysis Corporation own IMP's the cost of the IMP's and their network interconnect cost must also be considered Since ANTS's are Host computers to an IMP up to four ANTS's can be connected to a single IMP 4 CURRENT DESIGNS - TIP This section presents preliminary estimates of the costs of terminal access based on using TIP's as roots of centralized networks These estimates are made using the models developed in the previous section and the line-layout algorithm described in the previous report The number and locations of TIP's were heuristically determined by visual inspection of the network configuration The network model resulting from a combination of the model components presented in the previous section is described below 4 1 NETWORK MODEL - TIP As noted the currently designed TIP has no provision for the support of multidrop lines Both hardware and software modifications may be necessary for the acceptable addition of this capability Significant requirements are line protocol for the multidrop lines and more extensive file manipulation resulting from the larger number of terminals The line protocol must permit line utilization of approximately 50% a conservative figure based on the use of ordinary polling tech ig as for multidrop lines With the previously described traffic range of 10bps to 100bps this gives a possible range of 6 to 60 terminals on a line The sixty-three possible connected lines allow a maximum demand of 37 8 Kbps to be placed on a TIP by the terminals Using the maximum demand figure in the TIP bandwidth formula indicates that such a TIP would have sufficient additional bandwidth to support a Host and also be connected to the ARPANET in a manner consistent with current practices However the number of terminals a TIP handles in the maximum demand case 378 3780 is far beyond the current maximum configuration 63 This 3 16 Network Analysis Corporation increase in number should be anticipated as causing considerable additional overhead for file manipulation Furthermore additional overhead may be anticipated due to the burden of a multidrop line protocol Under these conditions the maximum number of terminals that a TIP can handle is assumed to be 630 one order of magnitude greater than its current direct connection capacity This gives a network model as below 4 2 TIP 1 up to 63 line connections 2 up to 630 terminals Lines up to 600 terminals line t where t is the traffic terminal in bps DESIGN RESULTS - TIP Cost is estimated as a function of the number of terminals and their traffic level subject to fixed TIP locations the multidrop line layout algorithm described in Semiannual Report #1 is applied to derive the multidrop line cost In the table below costs are given for a 100 terminal system at a traffic level of 100 bps each for different numbers of TIP's at different locations 100 Terminals 100bps each Monthly Line Costs Monthly Line Costs And TIP Rental # TIP'S Locations 1 Chicago Memphis New York $14 007 14 501 17 190 $16 5C 2 NY - LA 13 091 18 091 3 NY - LA - CHI NY - LA - MEM 11 375 11 302 18 875 18 802 17 001 19 690 These results show that a higher number of TIP's yields lower line costs but not necessarily a lower total cost Consequently the 3 17 fretwork Analysis Corporation number of TIP's is varied until a local minimum is reached Table 1 gives preliminary estimates of the cost of terminal connection as a function of the number of terminals and the level of traffic The size of the networks under consideration is at present being enlarged to refine these estimates Results are shown as points connected by straight line segments in Figure 5 The curves suggest that for low numbers of terminals and thus low numbers of TIP's the line constraints and TIP locations have significant impact on cost For large numb rs of terminals and thus larger numbers of TIP's costs - ce less sensitive to TIP placement and line constraint» Simplified illustrations of several of the network designs are given in Figures 6-9 Note that for low traffic 10bps it is cost effective to use as few TIP's as possible while for high traffic 100bps savings are achieved by using more than the minimum number of TIP's With low traffic many terminals can be chained together on one line to economically connect distant terminals to a TIP With high traffic only a few terminals can be placed on a line and distant terminals result in several long uneconomical lines Since TIP's are relatively expensive when compared to conventional multiplexers these simpler devices to achieve economy of scale will also be investigated as an alternative architecture 5 COST-PERFORMANCE TRADEOFFS Cost effective terminal access will depend on both sn effective line layout algorithm to connect terminals with access ports and on an effective port location algorithm to determine both the number and location of access ports The line layout problem for a given set of ports has been effectively dealt with in Part 1 of Semiannual Report #1 Present research is aimed at developing a port location algorithm to be combined with the line layout algorithm for complete network design The total algorithm will then be used to investigate network tradeoffs with up to 10 000 terminals and several hundred IMP's 3 18 TABLE 1 PRELIMINARY TERMINAL - TIP EXPERIMENT RESULTS Number of Terminals 10 Traffic bps 20 50 100 100 $ 13 095 $ 13 231 $ 15 146 $ 17 607 200 18 906 19 875 23 373 31 818 500 36 050 39 138 49 208 56 099 1 000 66 775 72 893 83 886 94 189 2 000 119 570 125 085 144 759 165 817 3 19 1 000 1 9 a 7 6 5 s 43 o u 100 1 10 1 t i i -i—i—i 6 789 1 3 4 iti» 5 6 7 8 91 yaoo io coo Number of Terminals FIGURE 5 PRELIMINARY ESTIMATES OF TERMINAL CONNECTION COSTS 3 20 i s C U z z H a H EH U H fa fa 0 a XI o fa Q O Z o o « o fa z o H w Q O EH fa Z « 3 21 ft x c •H Q X u 2 Z 0 H EH H 01 a XI o D H fa w Q O z © CM « o z uH w w Q « o s EH W Z 3 22 •J- s c ■A D Z Z M u H XI o D 01 w Q O z o o in « O 6M Z H en Cd Q g w Z -' 3 23 iJ 1 1 £ C o Ü u X u u z 2 H EH U H fa fa D O M fa a o o a a o z o o in « O fa z H CO w Q O ew z 3 24 I7I«VA i«an s s corporation CHAPTER 4 A CUT SATURATION ALGORITHM FOR TOPOLOr-ICAL DESIGN OF PACKET SWITCHED COMMUNICATION NFTWORKS PART I 1 INTRODUCTION The topological design of packet switched communication networks was first discussed by Frank Frisch and Chou Frank 1970 who described an effective method for findinc low cost topologies based on branch exchange techniques The overall design problem and the limitations of branch exchange techniaues were described by Frank and Chou Frank 1973 It has become clear that as networks grow new approaches are recuired to produce effective network desicrns In this chapter a new approach to the topological design problem is described This approach is based on a fundamental limitation on packet switched network performance called cut saturation The cut saturation property and its relation to network throughput and time delay were discussed by Frank Kahn and Kleinrock Frank 1972 and an efficient routing techniaue based on this principle was reported by Chou and Frank Chou 1972 The problem addressed in this chapter is the design of low-cost packet switched network topologies with a fixed number of sites Nodes and wi h single fixed-capacity communication lines Links The approach taken is a modification of the Branch Exchange Method The algorithm iteratively attempts to keep the network throughput within specified bounds while reducing the overall line cost and maintaining capacity delay and reliability constraints 4 1 e work Analysis Corporation The results show that 1 The cut saturation solutions are at least as good as the Branch Exchange Method BXC 2 The cut saturation technique is computationally much more efficient than the BXC technique 2 DESCRIPTION OF THE CUT SATURATION CS METHOD Constraints on network designs are 1 A fixed number of sites 2 All lines of one capacity say 50 Kbps 3 Maximum average delay per packet say 0 2 sec 4 At least 2-connectivity The heart of the CS algorithm is its routing algorithm The routing algorithm employed is an adaption of the Flow Deviation Method for solving non-linear constrained multi-commodity flow problems Fratta 1973 This algorithm which has been described in detail elsewhere provides optimal or near optimal link flows for a given traffic requirement network topology and link capacity allocation The object of the optimization is to achieve a desired network throughput at the lowest possible cost Given a typical network configuration usually at least 2-connected but much less than 3-connected subject to the network constraints the routing algorithm can be applied to obtain optimal link flows With these link flows some links will be highly utilized 80-90% while others will be underutilized If the links are ordered according to their utilization and tnen successively removed the network 4 2 Network Analysis Corporation will eventually be partitioned into two disjoint components of nodes The minimal set of these highly utilized links that disconnects the network is called a saturated cutset This experiment was performed a number of times It was continuously observed that the total traffic between these 2 components was usually very close to the sum of the flows in the saturated cutset links In other words if ND number of nodes in component i for i 1 2 RE node pair traffic requirement NC number of cutset links and f flow in cutset link i then NC ND x ND x RE l f 1 ' i 1 1 Clearly the saturated cutset imposes a physical limitation on the network throughput In fact a theoretical upper bound on RE corresponding to fully saturated links i e infinite delay is as follows MIN EC RE over _S S UD1 x ND2 '' „ ' K where C the capacity of cutset link k S any minimal cut and ND number of nodes in component i corresponding to cut S Since the links in the saturated cutset have f c- from 1 it follows that NC RE E C i 1 NDj x ND2 3 Thus • The value of close to the • Improvements the capacity RE given by the routing algorithm is very theoretical upper bound i e near optimal on RE can only be obtained by reinforcing of the cutset On the other hand a new link introduced within a component will not significantly increase the capacity of the cutset Therefore if we want to introduce links that will increase the capacity of 4 3 V tw ark Anah s j Corporation the cutset we must consider only the potential links that join the 2 components This guideline provides an efficient criterion for the selection of links to be introduced into the network 3 CUT SATURATION ALGORITHM IMPLEMENTATION The cut saturation algorithm consists of several basic sections 1 Routing - performed after each network modification to generate new optimal link flows 2 Saturated Cutset Determination - performed at each stage of routing 3 Add-Only - Select the Best'' link to jcin the two components The Add-Only operation is key to the basic CS method 4 Delete-Only - selects the best link for deletion from a highly connected topology 5 Perturbations - combines Add-Only and Delete-Only operations 6 Chain collapsing - replaces selected serial chains by a single equivalent link to improve efficiency of optimization 3 1 THE ADD-ONLY OPERATION The Add-Only algorithm determines the location of the link that will join the two components K and K„ The links that must be considered for insertion correspond to the pairs x y such that x e K y e K Using the cut saturation philosophy for throughput improvement while attempting to minimize the cost a reasonable choice for the new link is the one that while ioining the two components has the shortest distance i e the smallest cost as shown in Figure 1 4 4 Network Analysis Corporation Unfortunately this modification tends to shift the cutset see Figure 2 with little throughput improvement This effect will be further discussed in a later section A reasonable modification would be to connect the centers of traffic of the two components as shown in Figure 3 Here the center of traffic is defined as the center of gravity of the component when each has node weight proportional to its traffic requirement However for networks of medium and large size the centers of traffic are likely to be distant from the cutset and thus links joining them are costly 4 5 Xclwork Anolysv Corporation A simple heuristic technique to obtain the center of traffic effect is called Distance 2 This technique attempts to remove from the set of link insertion candidates the node pairs in which one of the nodes is close to the saturated cutset The method retains nodes from each component that are at a distance of at least two links from nodes adjacent to the cutset If this is not possible because of small component size nodes adjacent to a unit distance of 1 the cutset nodes are retained All nodes that do not satisfy this criterion are eliminated from the component Figures 4 5 Fifi where 4 £ node that has a link in the cutset ■% node adjacent to Q KS revised component obtained from K consisting only of nodes that satisfy ch3 distance 2 criterion 4 6 Network Analysis Corporation « z x M U 0 5 •u 0 W I c z w si U Q O 2 2 DJ 2 O S o u 4 7 Network Analysis Corporation Now the only links considered for insertion are links x y such that x c KS y e KS2 The distance 2 criterion retains nodes that are at least 5 links distant from each other since 2 unit-link distance from cutset for KS 2 for KS 1 5 cutset link A specific 26-node example of the distance 2 criterion is given in Figure 5 Another measure based on traffic considerations is called SDIS I J which is an index of the saturation of the least saturated path MI J from node I to node J This saturation of a path is defined as SDIS I J MIN for all ff I J it yJ C -f V - r i where T l j is any I J path and the sum is over all links in the particular path TT I J The values of all SDIS I J 's are readily provided by the routing algorithm The insertion of a link between a node pair I J with high SDIS I J is likely to achieve good throughput improvement because it provides an alternative to an already saturated path Here again as in the distance 2 criterion the tradeoff between throughput improvement and link cost must be considered 4 8 Hetwork Analysis Corporation Several Add-Only optimizations for a 26-node 30-link ARPANET topology were performed In one after ordering the potential links according to cost at each iteration the minimum cost links satisfying the distance 2 criterion were introduced In another after ordering the links according to the ratio cost SDIS the link minimizing the ratio was added These results are shown in Figure 6 and further Add-Only results are presented in Section 4 2 Surprisingly the second run gave exactly the same results as the first one Based on such findings it was concluded that the two criteria are almost equivalent for the network sizes under consideration and therefore the simpler distance 2 criterion was used for all further optimization 3 2 THE DELETE-ONLY OPERATION The Delete-Only operation begins with a highly connected topology and eliminates one link at each iteration thus continuously reducing throughput and cost The criterion for link removal is based on link utilization and link cost One approach is to remove the most expensive and underutilized link That is that link which when removed maximizes the quantity Ei A Di x Ci-fi C i is removed where D is the cost of link i C is the capacity of link i F is the flow in link i and C -fi is the relative excess capacity C If removal of this link results in the creation of a pendant or isolated node the link is not removed With this restriction if the original network is 2-connected the Delete 4 9 FIGURE 900 6 tV -N0DE ADD ONLY o 800 ■ t wen k rhi ouqhjn i Kbit 700 o 6 SO 000 00 o 450 70 80 _i_ 100 90 110 LINE COST $K MONTIl 4 10 120 rVeiWOfK Hliuiym v j Hv Only method results in a 2-connected network and if the network was connected it remains connected Finally if a very high cost link in the saturated cutset leads to a maximum E the link is not removed The results of Delete-Only and Add-Only experiments with 10 and 26 node networks are shown in Figures 7 and 8 Both delete runs were started from good highly connected topologies Considering that the two methods are conceptually very different the fact that resulting cost-throughput solutions are in the same range leads to the conjecture that both methods are near optimal 3 3 PERTURBATIONS Once a configuration has achieved a required throughput the designer would like to rearrange links so that throughput remains constant and cost is reduced The branch exchange technique provides one such method The combination of the Add-Only and Delete-Only algorithms provides another technique which will be called Perturbation Any exchange technique cannot be expected to keep throughput absolutely constant and therefore lower and upper bounds within which throughput is allowed to vary for intermediate solutions say 5% of the desired throughput are specified The approach taken allows one link to be introduced according to the idd-Only criterion and one link to be removed according to the Delete-Only criterion If throughput exceeds the upper bound a Delete-Only is performed Similarly an Add-Only is performed when the throughput decreases beneath the lower bound Therefore starting with any link configuration a desired throughput level is attained by either adding or removing links according to cost and cutset considerations After reaching the desired level links are rearranged so that cost is reduced and the desired throughput is retained 4 11 oA A o A A o A O o -I 1 » 1—H 2 1 ' ' 1 1 1 1 H 1 ■1 4 12 i IN f - UllA Tj- nNJ Y A - ADD-ONLY 1 • 1- FIGURE 8 26 - NODES rhroughput in KB SBC 1000 • 900 OA° BOO 700 o o OAA A O 600 500 OA DELETE-ONLY 400 - 300 - ADD-ONLY o o 200 « 65 70 75 80 —» 05 90 LINK 4 13 I 9r U T -t- 100 SK t » 105 110 MONTH » 115 ' 120 Network Anjh » Coloration Also considered during perturbation is the effect of Domination Network A dominates Network B if C CD and RAÖ A t RD where C and R are cost and throughput respectively Each network i can be characterized by an ordered pair P C R A list of the dominant points is kept to serve as a criterion Tor design modifications In fact during perturbation an intermediate network may be dominated by another previously generated network In this case the network is returned to the previous stage and the method is continued A flow-chart for the perturbation method ib given in Figure 9 An example of the application of the perturbation technique to a 26 node network is shown in Figure 10 3 4 CHAINS COLLAPSING Typical ARPANET configurations are at least 2-connected but much less than 3-connected Consequently there are many chains with 4-5 serial nodes The presence of chains can produce inafficiencies in the CS algorithm as shown later in this section There are two types of traffic on a chain 1 Internal Traffic corresponding to requirements from nodes internal to the chain to external nodes and vice versa and between internal nodes This component of traffic varies from link to link along the chain 2 Transit Traffic corresponding to requirements between external nodes which are routed along the cnain This traffic component is uniform along the chain The efficiency of the CS method is greatly enhanced i r some of the chains are collapsed and replaced by a single equivalent link FIGURL i READ IN VARIOUS PARAMETERS INITIAL I0P01OGY NUMBER OF INTEPATIONS DESIRED T I 0 I ROUTING ALGORITHM DETERMINES THROUGHPUT K CUTSET DETERMINATION CUTSET DETERMINATION CUTSET DETERMINATION HAT ABB sm J I PfitfTE DELETE ONLY 1 ROUTING HLGORITHM ADD BACK DELETE» LINK 4 15 I H '■ KV k-Al H I K i' r MAX o V • 2 18 1 19 Oi KO' GMPUT MIN o O lii EACH I'OINT DES I MATES THE I'UTSEF ITERATION THAT GENERATED TliE POINT o 'ART Di MIN ANT SO TT N ■ ■ L iO i Iv 4 16 LINE '0 'T K MOMTI 1 ill Network Analysis Corporation In particular chains with predominantly transit traffic should be collapsed Consider the network shown in Figure 11 with the saturated cutset indicated Notice that each cutset link belongs tc a different chain It can be shown experimentally that the traffic on such chains is prevalently transit traffic Therefore all links in a chain carry the same amount of flow and are uniformly saturated Suppose that the CS technique is applied One of the two nodes between which a new link is inserted may be internal to the cutset chain See Figure 12 The insertion then shifts the cut-set to some other link of the chain with very little throughput improvement since all links were uniformly saturated To avoid this the algorithm is modifying to disregard saturated cut-set chain nodes during link insertion Consider the example in Figure 13 Since chain links tend to be uniformly saturated the cutset shown in Figure 13 may be chosen by the CS method This could happen for example if flows in the upper chain are slightly greater than those in the other chains This selection is clearly improper since little throughput improvement can be obtained by adding a link across this particular cutset Again to prevent such a situation special attention must be given to chains during saturated cutset determination A remedy to the above situations is the chain collapsing technique which replaces a chain by a single link with equivalent link flow equal to the maximum of all link flows in the chain See Figure 14 This procedure is applied by the CS algorithm before cutset determination After cutset determination and before link insertion all collapsed chains are regenerated i e the internal nodes are restored except for the saturated cutset chains For example assuming that the saturated cutset in Figure 14 consists of the three intermediate chains before link insertion the network shown in Figure 15 is considered The collapsing technique handles pathological situations but there are cases when chains should not be collapsed Typically these are when internal traffic prevails over 4 17 v » tf$ X- m-t ■ - Network Anaiysis Corporation 111 not 11 FIGURE 13 4 18 Network Analysis Corporation transit traffic and therefore link flow is not uniform along the chain The following criterion öased on theoretical considerations and experimentation is used to determine when a chain should be collapsed A chain is not collapscble if 1 the number of intermediate nodes in the chain is larger than NN 3 where NN is the total number of nodes and 2 the ratio between maximum and minimum flow on the chain is larger than 1 5 To demonstrate the impact of chain collapsing on the CS algorithm consider the two 43 node ARPANET design examples shown in Figures 16 and 17 The first does not allow chain collapsing while the second does no chain collapsing L d F ■■£ l 4 20 Network Analysis Corporation For the example of Figure 16 the saturated cutset is represented by the three cross country chains However because of the chain effect the CS method is able to detect such a cutset only at step l d The plot in Figur« 18 shows cost and throughput for all the above steps the largest improvement is obtained from l d to I e -0 0- 2 fc FIGURE 17 For the Figure 17 example the proper cutset is detected at the first step and significant throughput improvement is immediately achieved See Figure 18 Notice from Figure 18 that the collapsing results are constantly better than the non-collapsing ones in the Add-Only phase below the minimum throughput threshold Above this threshold branch deletions and additions are performed and some of the bad initial choices of the non- oi -psing algorithm are deleted Therefore the results of the two algorithms in that range are comparable 4 21 '•-» • cf g M 8 to J 8 S o f OOj OÖ C OG in o J U Q O r- vc j« Z -H • in « o • 1 rn CN c I 3 0 i-l o c - •• jj H H « Oil 0 i u it 4 22 1 o c i i c o Network Analysis Corporation 4 OTHER DESIGN CONSIDERATIONS 4 1 RELIABILITY It has been shown in previous NAC reports that networks containing pendant nodes nodes of degree 1 are not sufficiently reliable No provision however is made in the CS algorithm to favor the connection of pendant nodes Nevertheless starting from network configurations of 10-26 nodes with many pendant nodes trees 2-connectivity is rapidly achieved This can be attributed to the fact that links incident to pendant nodes become saturated early in the design algorithm A pendant node link would constitute the cutset with the pendant node in one component and the rest of the network in the other component The only alternative for the Add-Only algorithm therefore is to establish another connection between the pendant node and the rest of the network Further study will focus on a better criterion to connect pendant nodes 4 2 STARTING NETWORK CONFIGURATIONS The input to the CS algorithm consists of various parameters throughput thresholds maximum number of iterations time delay tolerances etc Of considerable importance is the initial network configuration Several experiments using various starting topologies such as trees mimimum spanning trees and 2-connected topologies were performed The results given in Figures 19 20 and 21 show various solutions for 10 26 and 40 node networks The experiments for the 10 and 26 node case were run using the distance 2 criterion The collapsing technique was used for the 40 node case The starting link configuarioii could be crucial to the performance of any design algorithms The results however show that 4 23 u R ■ i - I' 'I FT i A E KUIiJR o A a O □ 4fin o a AD A A - TREES m Q- 2 CONNEiTKD ToroT onii- s 0Q -I ' 1 K 1 17 1 1H 1 19 1 20 1 —I 21 22 1 23 1 24 1- 25 1 2ft 1 27 LINE COST 3 MONT 4 24 _____________ 1 28 1 • h in 26 MODES DISTANCE 2 FIGURE 20 11004 1000 O A A 900 AO • a A ■ ■• 800 L a 0 « 700 J ■ A tiOQl g» A 0 SOQI 0° O 1 »■■ 2 CONNECTED INITIAL CONFIGURATION PERTUBATIONS - KIN SPANNING TIEE PERTURBATION A 40 4 a A 01 A m 8 O TREES JUST ADD MIN SP TREE JUST ADO « -4—1 60 h—I 70 1 80 1 1 90 1—H— —I—I—I 100 100 HO 120 ' A 13C LINE COST SK MONTK 4 25 ' « MMti0Uma S THRÜüGHPlT KBITS SEC l'IillP O O i- ■ i • ■ ' MJN P A A P A -i'DNNKiTKH STARTINC i ffl FU i M'lU O ■ ■ -UN M'ANNTHI TRKK A ' -' ■ 1 I —I 70 60 1 1 1 1 '10 ■ p 4 26 ■ ■- - 1 5 1 1 1 h 100 '• 13 0 S 1211 1 TNE rOS'V ' -' MONTH Network Analysis Corporation the CS algorithm is not sensitive to starting configuations since cost-throughput curves for different initial topologies aie close to each other The best starting topology seems to be a 2-connected one Further sensitivity studies will be performed with other starting configuations such as star and loop topologies and fully-connected networks The goal is to establish good standard initial topologies which depend on node location rsliability etc and to develop algorithms for the generation of such initial topologies to avoid the preliminary hand design 5 COMPUTATIONAL REQUIREMENTS FOR THE CUT SATURATION DESIGN 5 1 EXECUTION TIME The execution time per iteration which includes routing and cutset modification is dependent on the size of the network In particular the computational complexity C_ of the flow deviation routing algorithm used is CR « NN' 3 ß NA 2 4 where NN' number of nodes with degree 3 NA number of links and « and 6 are proper coefficients which depend on code optimization and accuracy required Faster routing algorithms can be used but this does net appear necessary at the present time The complexity C ap »roximatel y C - Y NA of the cutset modification algorithms is 2 5 4 27 Network Analysis Corporation where y is a proper coefficient which depends on code optimization In most practical applications NN' total number of nodes For sufficiently large networks it appears that « NN' 3 NA 2 2 and therefore the total complexity is C - 6 NA 6 where 6 6 Y • Per-iteration running times on a CDC 6600 are presented in tables 1-3 Equation 6 can be verified from the results in those tables Letting C be the running time we evaluate 6 as follows 6 ■ -C NA 2 FOR 10 NODES 20 links 6 — 0020 20r FOR 26 NODES 30 links 6 1 9 0021 POT 39 links 6 -2- 0016 39P FOR 40 NODES 54 links 6 61 links 6 4 4 ' 0015 54P 6 2 ' - 0017 61 Z The relatively small range of fluctuation of the coefficient justifies the assumption in equation 6 4 28 Network Analysis Corporation TABLE 1 If NODES Of Links Routing Cutset Total 15 3 2 5 16 4 3 7 17 4 2 6 18 4 3 7 19 5 3 8 20 5 3 8 In Seconds TABLE 2 26 NODES # Of Links Routing Cutset Total 27 1 2 5 1 7 30 1 2 7 1 9 33 1 4 5 1 9 36 1 5 7 2 2 39 1 8 8 In Seconds 2 6 rABLE 3 40 NODES # Of Links Routing Cutset Total 52 3 1 1 1 4 2 54 3 2 1 2 4 4 56 3 3 1 3 4 6 58 3 6 1 4 5 0 61 4 7 1 5 In Seconds 6 2 4 79 Network Analysis Corporation 5 2 CORE REQUIREMENTS The amount of core M needed for the design algorithm corresponds to the sum of various node and link arrays and is given by M 10 NN 2 3 NA 2 In addition the code requires 1ÜK words of core On the CDC 6600 the algorithm accomodates a 60 node 80 link network in 80 K words of core 5 3 LARGE NETS Computational and core requirements clearly set a limit to the size of the networks that an be solved directly with the prestnt algorithm Partitioning techniques are necessary for networks of 100 or more nodes 6 COMPARISON BETWEEN THE CS ALGORITHM AND OTHER EXISTING METHODS 6 1 INTRODUCTION To evaluate the efficiency of the CS algorithm CS results were compared to 1 2 theoretical lower results show that the other method and that Branch Exchange BXC algorithm results bounds and 3 manual network design The CS algorithm is more efficient than c ny it is indeed near-optimal 6 2 COMPARISON WITH BXC ALGORITHM The BXC Algorithm is an iterative network design technique At each iteration links are added deleted or exchanged and corresponding cost and throughput variations are computed If the tradeoff between the cost throughrut variation is favorable the topclogical modification addition deletion or branch exchange is accepted otherwise it is refused The procedure is exhaustive and terminates when no more improvement is possible 4 30 Network Analysis Corporation The major difference between BXC and CS is that CS considers only those link insertions and deletions that are likely to yield a favorable cost throughput tradeoff therefore the CS method can be expected to converge much more quickly to good solutions Another drawback of the BXC algorithm is the inaccuracy of the throughput computation after each 'ranch exchange in fact in order to cut down the computation time the BXC algorithm applies a suboptimal routing technique with throughput results 5% to 20% below optimum This inaccuracy can be misleading in the search for improved network configurations and requires that at the end of the BXC algorithm a large number of candidate solutions be re-evaluated with an optimal routing algorithm Three networks with 10 26 and 40 nodes respectively were designed using BXC and the results are compared to CS results in Figures 22 23 and 24 In no case was a BXC design better than a CS design In addition the IXC is much more time consuming than CS for the 40 node example the 11 BXC solutions required 450 seconds on a CDC 6600 while the 24 CS solutions required 118 seconds 6 3 LOWER BOUNDS Lower bounds on the cost of the optimal solution can be obtained by approximating the link cost capacity functions with concave lower envelopes and solving the associated concave multiconT odity flow problem with the aid of mathematical programming techniques Gerla 1973 in the specific case treated the link cost function is a step function and is approximated with a properly defined concave curve as shown in Figure 25 Clearly the minimum cost of the continuous concave design problem is a lower bound to the cost of the real problem because the concave link costs are always no greater than real link costs Notice Figures 26 and 27 that most CS solutions are within 5% to 10% of the lower bound 4 31 - '»• J i-i yir «vJ« 3rv A - i i'i f 11 i ■' • Ml'i IMA D 0 - i i FO M Ti O % i M D MOIH A l ° II ' Ö DDD □ 0 D b G D D A D D □ D D D D 4 32 MN ' OST K M -NT D ■ ' ■■ ' VICV ¥ o o o AA o o o '■ U UTION - w 85 'in OPTIMIZED SOLUTIONS 1 1— I Of I ' • ■ 'i - T TK MONTII 4 33 ■ «■- Fl UKK » I - G 950 o o o o o o 7- C A- CUTSET SOLUTIONi r ■ OPTIMIZED SOLUTIONS 7 Hi 140 ISO 145 LINE COST SK MONT 4 34 Network Analysis Corporation Considering that 1 the bcund is r ot very tight because concave costs are much lower than real costs and 2 the throughput of the concave solutions is exact v niie the throughput of the CS solution is within 2% to 5% ot optimum the strong conclusion is that the CS solutions are v ry near optimal CO -'T ' T D S £ C - o FIGURE r '0 r' bs CAPACITY r 4 35 ' ' ' •'■ ■■■' ■'■■ V i ' ' 900 riGL'R _'n A I - 4' ' A A AA - CUTSET SOLUTIONS A LOW K BOUND 2U INK i 0 T SK Mo -JT 4 36 ■ - W ii 'v-VisJK - w ' ''- 110 T i ' 'T FIUHW- -1 2» fiOVLr 1 'Ot Ai AAAA 71 I 6Ö0 i iDO CUTSET aül i ' IONS • LOWER BOUND -t- -f- no l-'o 1 H LINE COST $K MONTi 4 3 Network Analysis Corporation 6 4 MANUAL DESIGN In an attempt to improve CS solutions topological modifi- cations are often performed manually using in addition to the link cost and link saturation information available to the CS method human intuition In most cases however generated solutions had either poorer performance than previous CS solutions or were previously obtained CS solutions A conclusion therefore is that manual interaction is not required for good costthroughput results Interaction is still necessary however at least at this stage of CS algorithm development to deal with reliability issues that cannot be treated fully automatically e g break long chains etc 7 CONCLUSION AND FUTURE RESEARCH The cut saturation algorithm described is a novel method for the topological design of distributed communication networks A comparative analysis of this algorithm with respect to the Branch-Er change algorithm another well known technique for distributed network design shows that the former gives better results and is computationally more efficient than the latter Furthermore the comparison of CS solutions to theoretical lower bounds shows that the CS Algotithm is near optimal Although preliminary CS results were already very successful there is ample space for further research to improve tne present algorithm and extend its range of applications In particular required are techniques for generating good starting topologies considering a larger class of criteria for link insertion and deletion which might include some measure of network reliability performing more than one link addition and or deletion per iteration and providing interactive access to the design program via graphic terminals In addition the present CS algorithm will be extended so that it can be applied to problems with several levels of channel capacity and very large problems that require decomposition techniques 4 38 Network Analysis Corporation CHAPTER 5 COST COMPUTATION FOR NEW LINE TARIFFS AND SERVICES 1 INTRODUCTION With present line tariffs and network sizes the ost of a line or circuit in any data or computer communications network depends mainly on the direct distance between the two end points of the line Such is the case in the ARPANET Thu far it has been very simple to determine line costs However as new line tariffs are introduced as new types of transmission services are made available and as computer networks grow larger the line cost calculation will no longer be straightforward With some of the proposed new tariffs such as AT T's proposed Hi Lo density tariff the line cost between a pair of locations depends on a set of parameters which may not relate to distance Under the proposed new services mainly digital transmission and domestic satellite communications the user will be able to reduce cost by configuring networks in special ways Finally as a network's size grows advantage can be made cf line volume discount in its own right At present some networks achieve discounted rates on lines because they are part of much larger networks The immediate impact of these tariffs is that new computational techniques must be developed ho calculate line cost to evaluate and compare different tariffs and services and to configure least cost circuit routes On the surface it may appear that each tariff requires a special cost optimization technique However many tariffs can be placed in a generalized cost structure chat may be handled by the same optimization process On the other hand a design problem may involve more than one type of line cost structure A general design goax is to allow the network designer to subdivide on the 5 1 • Network Analysis Corporation basis of line tariffs the various line cost problems into a small number of classes each class corresponding to different cost structure For each cost structure a different computational technique general enough to handle all problems and tariffs corresponding to that cost structure is developed The global design program is obtained by combining the proper cost structure For example the line cost optimization for a 2-level satellite network would require 2 steps one corresponding to the satellite cost structure and one corresponding to the cost structure of the terrestrial subnetwork The purpose of this section is to classify possible cost structures and to propose outlines for future studies i developing computational techniques The emphasis is on the application of domestic satellite communications to large computer networks 2 NEW LINE TARIFFS AND THEIR IMPACT There are many new tariffs being proposed by AT T and various common carriers and domestic satellite companies The following three tariffs are typical 2 1 AT T's PROPOSED HI LO DENSITY TARIFF Approximately 37 rate zones are defined to be high density locations and the remaining are low density ones The cost per channel-mile for a line connecting two high density locations is less than one third of the cost between a lc - density location and any other location A low-to-low or iow-to-nigh ex - uit ran be implemented either by direct connection or by routinq 1 rough high density locations Since most nodes in a computer network are likely to be located in or near populated areas which usually are high density locations the network's line cost will be lower under this proposed tariff For nodes located in low density rate zones the network designer must decide how uo economically route circuits originating from these areas 5 2 Network 1n i i % urpcjuilion 2 2 AT T'S PROPOSED DIGITAL DATA SERVICE PDS This new data service being developed by AT T is based on the Tl digital carrier network Better quality and considerable economy can be obtained by transmitting data on the Tl rather than on traditional analog channels Initially DDS will be offered between 24 major cities and will be extended to most of the 370 high density locations mentioned before at a later date Different channel bandwidths can be leased at the following rates Bandwidth Kbs 2 4 4 8 9 6 56 0 Mileage Charge $ Mile x Mo 45 60 90 4 50 $ Mo Service Terminal 140 200 280 500 From a location where DDP is not available a customer can access the DDS network via a private analog channel of proper bandwidth and characteristics series 3000 5000 or 8000 and with adequate modems The cost for DDS s 56 KBPS line is less than that of a 50 KBPS line even at the Government Telpak rates Thus the availability of DDS will have an immediate cost impact on the ARPANET The greater impact will occur when Tl or T2 carriers are available for public service Then if a computer network is large enough Tl carriers can be used to concentrate traffic to channel high traffic volume or to time-division-multiplex TDM a Tl carrier into sub-channels 2 3 DOMESTIC SATELLITE SERVICE Several companies WU Amersat CML RCA GTE AT T have been granted FCC approval to sell private satellite communication services in the U S A Most satellite carriers will provide in addition to the satellite channel a terrestrial backbone network to facilitate satellite access and to improve overall reliability Although most ■ ■ - i J-iJ'- Htt Network Analysis Corporation satellite tariffs are not yet definitive it is anticipated that the total line cost wil be given by the sum of the satellite and terrestrial cost components In particular the satellite segment from antenna to antenna will be much less expensive than a coast to coast terrestrial channel e g a full duplex 56 KBS channel on the satellite will cost 500 $ Mo Different rates will apply depending upon whether the customer provides his own ground stations arranges for terrestrial access to the company's ground stations or finally uses the company's terrestrial network Two general characteristics of satellite rates are 1 rates not dependent on distance only and 2 strong volume discount with respect to satellite bandwidth used 3 LINE COST MODELS In the leasing of communication racilities the user is faced with a variety of alternatives differing in cost quality of transmission delay etc To achieve a minimum cost network design all such alternatives must be carefully considered It is practically impossible to develop computer programs for network design which would take into account all the available commercial offerings The best approach is to classify such c iferings into a limited number of very general cost structures and to develop efficient algorithms for each structure Specific problems can be solved by properly varying the input parameters of each algorithm Four classes of cost structures are identified distance dependent DID structures location dependent LOD structures volume discount VOD structures and hierarchical structures A description of the four classes follows A DID Structures The cost per channel from point A to point B is a function of distance A B only It is independent of the specific locations of A b and of the number of channels or bandwidths from A to B For practical purposes circuits in the ARPANET can be 5 4 Network Analysis Corporation estimated in this manner even though the ARPANET'S circuits are mostly routed through existing governmental Telpak circuits Other examples of DID structure are the type 3000 tariff and the type 8000 tariff If we restrict A and B to belonging to a privileged set of points the Hi Lo density tariff where A and B are high density points can also be considered as a DID structure B LOP Structures The cost per channel from A to B depends on the specific locations of A and B It is independent however of the number of channels or bandwidths from A to B no volume discount A typical example of a LOD structure is the Hi Lo density tariff When either A or B or both are low density points the rate depends not only on distance A B but also on the geographical position of A and B with respect to high density points In problems where only one channel of a given capacity must be allocated between A and B md therefore a volume discount does not apply the DDS tariff and in general all specialized and satellite carrier tariffs used in conjunction with AT T tariff can be considered as LOD structures In fact the cost of the channel will depend on the relative position of points A and B from the DDS network and on the special carrier network or terrestrial backbone network of the satellite company In essence this is a shortest path problem Finding a least cost circuit between a ncde pair is equivalent to finding a shortest in cost path that connects the two This path may contain other intermediate nodes if necessary C VOD Structures The cost of leasing an additional channel or additional bandwidth from A to B decreases with the volume of channels or bandwidths or channel-miles already leased from A to B Furthermore the cost depends on the distance between A and B but does 5 5 - ■ — Mi -- fc v w„ - - 4 Network Analysis Corporation not depend on their specific locations Examples of VOD structures are the Telpak tariffs where A and B can be any locations in the U S A the DDS tariff where A and B belong to the DDS network ar J the specialized carriers and satellite companies where A an- B belong to the respective networks There is no exact method for solving optimization problems with such cost structures A basic heuristic approach is to iteratively compute shortest routes according to appropriate link costs which change from iteration to iteration and redistribute or deviate requirements on such routes The effect of such deviations is to achieve better economy of scale and therefore reduce cost Without going into detail we simply mention that the efficiency of the VOD algorithms depends strongly on the nature of the cost-capacity functions of the links In particular link functions which are rather irregular neither concave nor convex and with large capacity jumps like the Telpak case shown in Figure 1 are in general difficult to handle during network design On the other hand link functions with small capacity -jumps and which can be reasonably approximated by a concave curve see Figure 2 lead to quite efficient algorithms Although optimal topology will depend on many factors economy of seal3 throughput level node geographical locations requirements etc it is possible to anticipate that cost structures with strong economies of scale lead to tree topologies while structures with mild economy of scale lead to highly connected topologies D Hierarchical Structures Partitioning and Node Location Problems Network partitioning consists of dividing the nodes into subsets and solving a separate design problem for each subset This operation also requires the solution of a location problem 5 6 - iirt»w if-j -'niTiFirtir i- -jj ilij 'tfl '■liiiMlitflüTnuiurfe Trmirm- it - Network Analysis Corporation Capacity FIGURE 1 i FIGURE 2 Capacity 5 7 ■ ' „■ ■■ - -j# jS V Network Analysis Corporation because partitions are connected to each other or to a central node through one or more exchange nodes whose locations must be optimally selected Hierarchical structures and network partitioning are the natural consequences of a VOD cost structure or more generally of any economy of scale situation where it pays to implement a two-level hierarchical structure with several low level networks and one high level network Traffic between low level networks is sent to the exchanges and from there to the high level network The high level network links carry a high traffic volume and can achieve a better volume discount than can links in low level networks 4 AN ALGORITHM FOR OPTIMIZING DOMESTIC SATELLITE COMMUNICATIONS NETWORKS FOR COMPUTER COMMUNIC% TIONS-PART 1 There are three possible ways to extract from the satellite channels to be used in a computer network from a dornesti c satellite company's central offices from a small roof top antenna it each terminal site node and from strategically located ground stations which are set up specially for th - network The first approach is treated in Chapter 2 of this report The second approach will not be feasible in the near future since current antennae under 45 feet in diameter can receive but cannot transmit adequately at high data rates This subsection addresses the third approach In this approach all four cost structures described in the last subsection are encountered Nodes are partitioned and a ground station is located in each partition For the terrestrial network volume discounts may be used to connect nodes to the ground stations location dependent structures may be used to calculate line costs for the possible high low density tariff for connecting lines between different common carriers and between private microwave links and common carriers finally costs for some lines can always be determined by direct distances distance dependent structures f Network Analysis Corporation Tc solve the problem stated above a computer optimization program is necessary Figure 3 shows a flow chart for a proposed program The function of each block of the flow chart is described below This description is intended to demonstrate the logical flow of the program rather than to provide complete details for each U ock A Data Base The Data Base contains engineering data and cost information for termination and communication channels it also contains V-H coordinates B U er Inputs Information input by users includes Network Information This includes types of communication devices engineering data costs and V-H coordinates if not already in the data base Traffic Requirements Traffic requirements can be expressed as number of accesses number of channels bandwidth requirements or data bit rates at a terminal location or between a pair of locations If available traffic variations as a function of time should also be included Design Restrictions Preassigned terrestrial links preassigned earth stations sites allowable earth station locations and the number of earth stations are among possible constraints to be imposed on each design Such restrictions may be the consequence of previous designs or may be derived from other considerations 5 9 c «»S» i sV ■ - Det Clusters with Max Inter-Cluster Costs © Det the Median for Each Cluster © I © Det the Median and the Associated Clusters © Recluster Det the Medians and the Associated Clusters I Det Earth Station Location © © Det Cost © Perturbation '© Choose the Best Partitioning © © © 1 Solve one Terminal Telpak for Each Cluster I I Post-Processor Output FIGURE 3 5 10 ■ ■ -' IV i «B © L © Det Earth Station Location Det Cost ctwork Analysis Corporation • Other Relevant Data C Program Manager The Program Manager manipulates user inputs and appropriate portions of the data base and creates a new data base in a format for use by the main body of the program D Traffic Requirement Specifications Traffic may be specified exclusively in terms of traffic per terminal pair In this case the algorithm used to locate earth stations is different from the one used when traffic requirements are specified in other terms When only terminal pair i e point-to-point requirements are specified the sequence F G H I J K identified in the flow chart is used to determine earth stations This sequence represents the algorithm for this traffic requirement specification E If requirements are specified in terms of total traffic at each terminal the algorithm sequence L M N 0 P Q is used to determine earth station locations If some requirements are specified in terms of traffic per terminal pair while others are specified in terms of total traffic per terminal two different approaches represented by sequences F G H I J K and L M N 0 P Q are used to find locations for earth stations and the least cost set is chosen as the final result F Terminal Partitioning The terminals involved at this stage are those whose traffic requirements are expressed in terms of traffic per terminal pair There may be other terminals in the network whose traffic requirements are defined differently These are considered for partitioning at a later stage If satellite links are not present requirements can be satisfied by connecting a direct 5 11 Network Analysis Corporation least cost terrestrial link with a capacity equal to the traffic requirement for that pair Some of these links may be routed through Telpak circuits for cost reduction The goal of the design syste'n is to reduce communications costs by replacing some of the terrestrial links with satellite links If terminals of this terrestrial network are partitioned into clusters and one earth station is placed in each cluster replacing only those terrestrial link interconnecting clusters may result i i cost savings Therefore the more traffic between clusters and the longer the links connecting the clusters the larger the potential cost saving That is the higher the communications costs for terrestrial links interconnecting clusters the higher the potential cost saving achieved by their replacement with satellite links The steps involved at the present terminal partitioning stage involve the partitioning of the terminals of the terrestrial network in such a way that the costs for the terrestrial links connecting the terminals between different clusters is maximized There is no exact method to achieve the above goal However there exists an iterative algorithm which gives very good results The number of clusters or the number of earth stations is not determined at this stage It is defined at the Program Manager stage G Center of Gravities A good heuristic for locating earth stations is to place one at the center of gravity or median for each cluster The object is to determine the center of gravity to locate earth stations so that the total terrestrial link cost for connecting terminals in the cluster directly to the station is theoretically minimum Each link cost is a function of distance and traffic requirements After all medians are found one may discover that lower cost connections for some terminal 5 12 ■■' ■ ■ '■ - - •■ ■ ■ ■ ' ■'■■ ■■ Network Analysis Corporation pairs are direct point-to-point terrestrial links rather than satellite links If such terminals exist their requirements are deleted from consideration and a set of new centers is determined H Checking Traffic Requirements If there are no terminals whose traffic requirements are expressed in terms of total traffic required at the terminal the clustering is finished Otherwise these terminals must be added into the clusters generated at step G I I i Reclustering In this step reclustering for the additional terminals and determination of new centers of gravity of the clusters is accciilished The terminals defined in K are added to clusters obtained in F so that the total cost of connectinc each cf the terminals to its corresponding center of gravity is minimum Each of the connections is a function of distance and traffic requirements J Determining Earth Station Locations The medians of the clusters are heuristically good locations for earth stations In practice there are restrictions on allowable locations for earth stations The allowable location nearest to each median is chosen as the potential site for an earth station K Determining Tentative Costs The costs to connect each terminal to the nearest earth station through a terrestrial link with sufficient capacity to traffic requirements is determined 5 13 Network Analysis Corporation L Clustering and Center of Gravities The definition of medians is stated in G Terminals are partitioned by some simple sets of rules into clusters The number of clusters is equal to the number of earth stations supplied by the Program Manager Terminals are iteratively shifted between clusters to minimize the total cofts to connect each terminal to its nearest median with a terrestrial link satisfying the traffic requirements At this stage terminals whose traffic requirements are specified in terms of traffic per terminal pair are not included in the clustering process M Checking Traffic Requirement Specifications If there are no terminals whose traffic requirements are given in terms of traffic per terminal pair no further clustering process is needed Otherwise reclustering may be necessary N Checking Requirements for Reclustering If any of these terminal pairs with pair wise requirements are in the same cluster or if any such terminals are not contained in any of the clusters further clustering is necessary 0 Terminal Reclustering Each of the terminals not contained in any of the clusters is assigned to the cluster whose median is closest If there is a direct traffic requirement between a pair of terminals and if they are in a same cluster the traffic requirement can be satisfied less expensively via terrestrial links only These requirements are deleted from consideration then calculated A new set of medians are P Determining Earth Station Locations Identical to Step J Q Determinining Tentative Costs Identical to Step K 5 14 Network Analrsis Corporation R Choosing the Least Cost Partitioning If only one type of traffic requirement is specified there would be one set of earth station locations and the program can proceed to the next block If both types of traffic requirements are specified there would be two sets of earth station locations The total cost to connect terminals with terrestrial links directly to their associated stations is different for the two sets The set of locations and their associated clusters corresponding to the lesser cost is chosen S Solving the One Terminal Telpak Problem The possibility exists that several terminals in the same cluster can be connected to the earth station by a shared wide band line The cost optimization associated with this situation is called the One Terminal Telpak Problem The problem complexity is such that in general only heuristic solutions are possible T Post-Processor This portion of the Programming System determines whether the earth station location for each cluster should be perturbed by proceeding to block U or whether systems with a different number of earth stations should be evaluated by returning to block C If no further processing is needed the results are placed into the desired format a complete cost analysis is performed and the plotting routines are called i U Perturbation With Telpak-like circuits included the earth station locations determined earlier may not be the least cost choices These locations are perturbed to test for possible cost reductions Also it may be less costly to connect some terminals near boundaries or the clusters to the earth station of a different cluster via a Telpak-like route 5 15 -ii S fc fci' Network Analysis Corporation CHAPTER 6 ROUTING CONSIDERATIONS FOR LARGE NETWORKS 1 INTRODUCTION In this chapter the computational aspects of the large network routing problem are considered Both hierarchical and nonhierarchical networks are studied and computation storage and overhead traffic requirements are examined Several hierarchical routing algorithms are proposed These algorithms are based on a decomposition approach and provide significant savings in memory space and computation time when compared to other techniques which have been implemented or proposed These algorithms can operate efficiently for distributed networks with 1000 or more nodes each of which is active in the routing process In a packet-switched communication network the routing policy is defined as the set of rules that guide each packet through the network along a route from source to destination We distinguish two types of routing policies deterministic policies which implicitly assume time invariant input rates and a perfectly reliable network configuration and adaptive policies' which are capable of adjusting to traffic fluctuations and network failures The former type policy can be specified analytically and is mostly used for network analysis and design Adaptive routing procedures protect against network failures and load fluctuations and thus are essential for traffic management in a network implementation An efficient routing policy should be able to fully utilize network capacity for any load pattern by sending packets on minimum delay or maximum throughput paths and eventually distributing heavy traffic on multiple paths However 6 1 Network Analysis Corporation the routing strategy alone cannot prevent network congestion if input traffic exceeds network capacity Therefore a flow control mechanism is needed to control input rates before congestion occurs Routing and flow control techniques have been designed and implemented for small and medium size nefworks up to about 64 nodes with satisfactory results However for networks of more than 100 nodes existing techniques become inefficient primarily because of computation time and memory space In fact the analytical solution of a deterministic routing problem with existing routing algorithms requires an amount of computation between NN 2 and NN 3 and a memory space on the order of NN 2 where NN is the number of nodes Similarly the implementation of the existing adaptive routing techniques for traffic management introduces an overhead proportional to NN The adaptive routing program presently used in ARPANET for instance requires at each nodal processor a storage space for routing table storage and a processing time for routing computation both proportional to NN similarly each node periodically transmits an amount of routing information proportional to NN The total overhead traffic obtained by multiplying the overhead of each node times the number of nodes is therefore proportional to NN The relation between network congestion and network size cannot be expressed in simple quantitative terms However it can be shown that in a large network under particular traffic conditions present flow control procedures are not able to prevent congestion of regional or local areas New routing and flow control techniques are therefore required for large networks Such techniques wixl in general use decomposition concepts tc reduce the large network problem to a set of dependent smaller problem each solvable using the existing methods 6 2 Network Analysis Corporation The overall solution should depend not only on network size but also on network topological structure In fact some solutions appropriate for a distributed structure such as a grid topology might not be efficient for a hierarchical structure Hierarchical structures are particularly advantageous for large network analysis and design Thus in this paper we concentrate our discussion on various hierarchical routing algorithms 2 HIERARCHICAL STRUCTURES A variety of topological structures can be used for network design ranging from hierarchical structures to uniformly distributed structures such as grids The preliminary 1000 node network study in NAC's Semiannual Report #1 has shown that hierarchical structures are desirable for large networks because 1 they are more economical 2 they are easier to analyze and design 3 they offer more flexibility in the choice of the system configuratÄp because different hierarchical levels can be implemented using different communication technologies and under different system requirements Because of the above factors a hierarchical structure was selected or the present large network routing study Without loss of generality it is assumed that there are two hierarchical levels the regional and the national level consisting of m regional networks with m nodes each connected to each other by a national network Each regional network is connected to the national network through two exchange nodes Therefore the national network has 2m nodes which are exchange nodes and belong both to regional and national networks 6 3 Network Analysis Corporation It is also assumed that flows between two nodes belonging to the same region cannot be sent along routes containing nodes external to the region he assumption is both physically realistic and also greatly simplifies both the deterministic and adaptive routing algorithms While a variety of other assumptions are possible reasonable ones do not seem to either substantially increase or decrease the difficulty of the routing problem 3 DETERMINISTIC ROUTING POLICIES The Deterministic Routing Problem The optimal deterministic policy is generally defined as the routing policy that minimizes the average packet delay T for a given external traffic requirement or alternatively as the policy that accommodates the maximum throughput svicn that T T__ where T__„ is the maximum admissible packet delay We assume that the basic traffic requirement is known and is given by an NN x NN matrix R° where R° i j is the average packet rate from source i to destination j The traffic that the network can actually accommodate is given to R A pR° where p is the admissible traffic level To maximize the throughput corresponds to maximize p Under appropriate assumptions whose validity in practical network implementations has been verified experimentally it is possible to obtain simple expressions of the delay T in terms of the average link flow rates One such expression is NA T IY E i l where £ -icrf 1 Hi oi- ' er of links Y total external input rate packet sec f average rate on channel i bits sec C- channel capacity of link i bits sec 6 4 Network Analysis Corporation More detailed traffic models lead to more elaborate expressions of T however the conceptual difficulty of the routing problem remains the same Using the appropriate expression for T the deterministic routing problem can be formulated as a convex multicommodity flow problem whose solution if it exists is unique Efficient algorithms exist for small and medium size networks Typically the routing policy for a 30 node network is obtained after 5 to 10 iterations and requires 2 to 4 seconds CPU time on a large computer However storage requirements and computa2 tion time increase at a rate on the order of between NN 3 and NN Therefore such algorithms are not adequate for the solution of networks with several hundred nodes Hierarchical Routing Algorithms If the network structure is hierarchical it is possible to develop hierarchical routing 2 algorithms with computing time proportional to NN and 3 2 memory space proportional to NN ' An example of hierarchical routing algorithm based on the flow deviation method is discussed below The algorithm takes advantage of the fact tnat regional traffic can use only regional links and it provides an exact solution to the problem of finding the routing that minimizes the average packet delay given the external requirements HFD Algorithm Step o Let £ be a feasible NA-dimensional link flow vector Let T° AT £° average delay corresponding to flow ° Let n 1 Step 1 Compute the NA-dimensional length vector l_ where l- is the equivalent length of link i as follows £n1 A EL 1 2 - VM - 6 5 ' '•'•— - Ji - ä Jfc 1 Network Analysis Corporation Using eq 1 Y 1 we have — Ci-r--1 2 notice that £ increases with channel saturation Step 2 Compute Shortest Routes m shortest route problems one for each region are first solved Using in part the regional results the shortest route problem for the national network is then computed Step 3 Assign link flows Flow requirements between node pairs are assigned to the shortest routes as computed in Step 2 The assignment is performed in 3 phases in phase 1 the equivalent national requirements between different regions are computed in phase 2 flows are assigned to national links and the equivalent regional requirements are computed in phase 3 flows are assigned to regional links The resulting flow is represented by an NA-dimensional vector _tj _n Step 4 Minimize the delay Let Tn A min T X£n_1 1-X $n X s t 0 X 1 4 Let X be the minimizer of Eq 4 let £ n A T£n-1 1-X cf n Step 5 Stopping rule If T - T _ e where e is a proper positive tolerance stop £n corresponds to the optimal deterministic routing within tolerance e Otherwise let m m 1 and go to Step 1 6 6 Network Analysis Corporation The HFD algorithm can be proven to converge to the optimal solution Notice also that the assumption that regional traffic never leaves the region is satisfied by the regional flow assignment performed in Step 3 Another hierarchical routing algorithm can be developed from the cut-saturation technique describsd in this report The algorithm called Hierarchical Cut-Saturation HCS algorithm maximizes network throughput at saturation The structure of HCS is very similar to that of HFD and the fundamental steps are the same HSC Algorithm Step 0 Initialization Let p° 0 Let 1° 0 Let n 1 Compute equivalent length vector I Step 1 as follows 1 if link i is not saturated n £ l °° if link i is saturated Step 2 Compute Shortest Routes Step 3 Assign Link Flows Step 4 Increase the Throughput Let £n Same as in HFD Same as in HFD £n_1 6£n Where 6 is the largest positive coefficient such that one or more links previously non-saturated reach saturation T„ p n „n-1 Let p o 6 7 Network Analysis Corporation Step 5 Stopping Rule Let S be the set of saturated links If the removal of S makes the network disconnected Stop • Otherwise let n n 1 and go to Step 1 Computational Considerations In nonhierarchical routing algorithms the computational bottleneck is represented by the shortest route computation and by the flow assignment the first requiring a number of operations between NN 2 and NN 3 depending on the degree of network connectivity and the second requiring a number of operations proportional to NN 2 In the two hierarchical algorithms HFD and HCS previously described shortest route and flow assignment are still the computational bottlenecks However it can be easily seen that both shortest route computation and flow assignment require from NN ° 2 to NN 2 operations The total memory space needed to store routing distance 2 and requirement matrices is proportional to NN in a nonhierarchical algorithm and to NN 3 2 ' in a hierarchical one The computation and storage reduction obtained with HFD and HCS allows the solution of the routing problem for 2-level hierarchical networks with a number of nodes on the order of one thousand which could not possibly be attacked with the traditional routing algorithms In the case of larger networks three or more hierarchical levels must be considered in order to obtain algorithms implementable on the computer 4 ADAPTIVE ROUTING POLICIES 4 1 NON-HIERARCHICAL POLICY Several types of nonhierarchical adaptive policies can be implemented on a packet switched communication network 6 8 9 J Network Analysis Corporation Here we use as a model the distributed adaptive policy presently used in the ARPANET In a nonhierarchical adaptive policy each nodal processor i i l NN stores an NN x A delay Table DT where A- is the set of nodes adjacent to the node i The entry DT k £ is the estimated minimal delay from node i to destination k if I is chosen as the next node in the route to k From DT an NN dimenstional minimum delay vector MDV11' is computed by the nodal processor as follows MDV i MDV 1' k 4 Min DT l £eA l k I for all k l NN k represents the minimum estimated delay from i to k and the corresponding £ is the next node in the route to k Periodically each node asynchronously transmits the vector MDV 1' to its neighbors Upon reception of neighbor's vectors node i updates DT as follows DT l k £ d i Jl MDV i k ' for all k l NN where d i £ is the measured delay queueing transmission on link i £ To perform the above operations an amount of computation a storage space and an exchange of routing information proportional to NN are required at each node 4 2 A CENTRALIZED ADAPTIVE POLICY The centralized adaptive policy here proposed is essentially a deterministic policy which is periodically updated according to load fluctuations and network failures Thus each node has a deterministic routing table a Network Routing Center NRC collects network information computes routing policy corrections according to such information and transmits routing update messages to all nodes For additional failure protection the nodes are also equipped with Minimum Hop Tables 6 9 Network Analysis Corporation Following is a description of possible specifications for a centralized adaptive policy implementation 4 2 1 Basic Operations Each node transmits to NRC asynchronously every 5 seconds the following information • number of packets transmitted on each output channel in the past 5 seconds • for each destination k the number of packets diri'ted to k which were received from external sources Host computers terminals etc in the past 5 seconds Using the information received from the nodes a computer available at the NRC site evaluates channel and external input rates averaged over the past 10 seconds Every 10 seconds the above data is fed to a routing program resident in core The routing program can be the Flow Deviation algorithm in such a case the program computes on the basis of channel traffic and external requirement for each node-destination pair the new route on which a fraction of the traffic say a 0 _ a 1 must be deviated in order to improve network performance At the end of the computation which typically requires 100 to 300 msec NRC delivers to each node a routing update message which contains • a vector of next nodes one per destination to which a fraction a of the incoming traffic must be deviated • the parameter a 6 10 J Network Analysis Corporation Upon reception of the routing message each node updates its routing table Since the Flow Deviation algorithm is an optimal routing algorithm the centralized adaptive policy converges to the deterministic policy in steady network conditions 4 2 2 Line and Node Failures In order to avoid congestion when a failure occurs in the 10-second interval between routing updates a very simple local adaptive policy is provided as a backup For example the minimum hop number policy During normal network operation no failures the min hop policy remains inoperative Is soon as a node experiences the failure of an output line or neighbor node 1 it modifies its min hop numbers according to the failures 2 it transmits immediately the min hop table to the neighbors 3 it switches from centralized adaptive to min hop mode of operation i e it routes the packets along min hop routes Gradually all nodes switch to min hop policy until the NRC learns about the failure New tables are then computed which account for the failure and the centralized adaptive policy is gradually restored During the transient period following the failure min hop and centralized adaptive policy co-exist in the network It can be easily seen that such a situation is logically acceptable and does not create severe performance degradation 4 2 3 NRC Failures The reliability of NRC can be improved by providing a backup NRC at another network site When one NRC goes down the backup takes over Furthermore if network failures isolate the NRC's so that they belong to two disconnected components each component can be 6 11 ■ vmt l lv '- - -■'■ -■ ■ - ■ ■ Network Analysis Corporation controlled by the respective NRC Finally if both NRC's go down or if a network component becomes disconnected from both NRC's packet routing is accomplished by the min hop policy 4 2 4 Centralized Versus Local Adaptive Policy Following are a few points of comparison between centralized adaptive policy CAP and local adaptive policy LAP • » Overhead traffic due to transmission of network status and routing information is approximately the same Processor overhead corresponding to routing and updating is of the same order of magnitude for both systems except that in LAP the routing computation is distributed among the nodes while in CAP it is performed by NRC In the transient period following each failure CAP is less efficient than LAP However failures typically occur at the average rate of one every two hours in a thirty node network Therefore the effect of failures on average CAP performance is not substantial CAP has no loops and makes efficient use of alternate paths LAP can generate loops and tends to use only one path at a time 6 12 -■ ' --■ -■■ ■■■ reaa iifr»i»MiWB ■ ' w 'J- -' ' ' ' ' «rt»ü Network Analysis Corporation • CAP can perform a better and more selective flow control on the external input rates than LAP as it has the global knowledge of all external traffic requirements 4 3 HIERARCHICAL POLICY A hierarchical adaptive policy consists of the combination of several regional policies and one natir al policy properly interfaced with one another at the exchange nodes Packet routing within each regional network and in the national network is performed according to the traditional algorithms Some new operations are required for the delivery of packets between different regions An outline of the hierarchical routing procedure is given below • Regional Routing Each node of a regional net uses and updates in the traditional fashion a regional routing table where only destinations within the region are listed Furthermore the node receives a national minimum delay vector from each of the two exchange nodes indicating the minimum delay from the exchange ncde to any region Packets with destination within the region are routed according to regional routing tables If a packet is directed to another region the source node determines after inspection of regional and national delay vectors the exchange node which minimizes the sum of regional and national delay and transmits the packet to it From there on the packet is handled by the national routing algorithm 6 13 «■» »K - ■ _ AMI Network Analysis Corporation National Routing Each exchange node in addition to regional routing and delay tables of the region to which it belongs is equipped with national tables which show routes and minimal delays to all other exchange nodes Using the national delay table each node computes the national minimum delay vector and propagates it among the nodes of its region Furthermore each exchange keeps track of the nodes of its region that it can reach through a regional route and stores the information in an m-dimensional regional connection vector The i-th entry of the vector is 0 if regional node i is unreachable because it is down or disconnected it is 1 otherwise As soon as a change in regional connection occurs the exchange node updates its connection vector and sends an updated copy of it to the other exchange node in the same region Each exchange node therefore stores two connection vectors one indicating the regional nodes reachable from itself the other indicating the regional nodes reachable from the other exchange node in the same region From the inspection of these vectors an exchange node upon reception of a packet directed to a node in its region determines whether 1 the packet can be directly delivered to the regional node or 2 must be routed through the other exchange node or 3 cannot be delivered because the destination is not reachable from either exchange node In the last case the packet is discarded and a negative acknowledgment is sent to the source node 6 14 ■V V S'-■-■■'-■ ' - M i A VVir' 3 Network Analysis Corporation The main difference- between a nonhierarchical ind a hierarchical policy is therefore represented by the existence in the latter of national minimum delay vectors in the regional nodes to determine the shortest way out of the region and of regional connection vectors in the exchange nodes to ensure reliable delivery of packets between different regions whenever a source to destination path exists 4 4 COMPUTATIONAL CONSIDERATIONS In the nonhierarchical case the overhead nodal processing storage space exchange of routing information for each node is proportional to NN In the hierarchical 2 case such an overhead is proportional to NN where NN m as usual The overhead reduction is obviously considerable and should allow the implementation of 2-level hierarchical adaptive routing algorithms on networks with on the order of a thousand nodes For larger networks it might be necessary to use hierarchical structures with 3 or more levels and modify the routing algorithms accordingly 5 CONCLUSION AND FUTURE RESEARCH In this chapter the computational aspects of large network routing have been considered and various hierarchical routing algorithms have been discussed The algorithms are based on a decomposition approach and provide significant savings on memory space and computation time with respect to the craditional techniques Such savings allow the application of the algorithms to networks with a thousand or more nodes Many other large network routing aspects remain to be investigated including 6 15 Network Analysis Corporation Multilevel Structures For very large networks the computational reduction obtained with a 2-level topology might not be sufficient In such a case multilevel hierarchies must be investigated similarly network reliability provided by two exchange nodes per region might not be adequate and configurations with 3 or more exchange nodes might be required However the selection of number of levels and number of exchange nodes will depend on many other design factors beside routing computational considerations High Bandwidth Traffic Channel capacities in regional networks are generally much smaller than channel capacities of the national network Consequently whenever a high bandwidth requirement arises between two nodes belonging to different regions a bottleneck is most likely to occur in the two regional networks Therefore to improve high bandwidth performance further research is required to develop efficient regional adaptive routing algorithms which provide multiple routes between high throughput nodes anc regional exchange nodes Flow Control As another consequence of lower regional capacities regional networks can become congested much sooner than the national network For instance if several nodes belonging to different regions simultaneously send packeto to the same destination the destination region might become congested and all the nodes in such a region unable to communicate with each other much before the sources learn about it The flow control technique currently implemented in ARPANET is based on a reassembly space reservation scheme It is aimed at 6 16 Network Analysis Corporation multipacket messages and cannot prevent regional congestion generated by single packet messages Therefore more efficient hierarchical flow control techniques should be investigated Such techniques might involve metering of traffic entering each regxon at the exchange nodes and circulation among national nodes of traffic load tables which reflect the load status of each region Use of Different Communication Techniques In the design of large multilevel hierarchical structures it is often more economical to use different communication techniques at different levels For example one could conceive a 3-levei system where the national level uses packet satellite communication the regional level uses pajket switching communications and the local level uses broadcast radio techniques New more general techniques must therefore be investigated 6 17 --• ■ Network Analysis Corporation CHAPTER 7 ROUTING ALGORITHMS FOR HIGH BANDWIDTH TRAFFIC 1 INTRODUCTION When a high volume data transfer must be performed between two high speed devices at two different ARPANET sites the total time of the transfer and therefore the efficient utilization of the devices can be considerably improved if data traffic between the two sites is routed along two or more routes so as to best utilize the excess capacity of the network This task often referred to as alternate routing must be performed by the routing algorithm resident in each IMP 2 DISTRIBUTED AND CENTRALIZED ROUTING ALGORITHMS The routing algorithm presently used in ARPANET and the new routing algorithm proposed by BBN can be classified as distributed routing algorithms Traffic is sent on shortest routes computed according to some reasonable length criterion the shortest route computation however is distributed in the sense that the computation at each node is based in part on the results of similar computations at neighbor nodes An alternative to the distributed algorithm it the centralized algorithm proposed earlier Such algorithm assumes the existence of a network routing center that collects all appropriate traffic information computes shortest routes between all node pairs and distributes routing information to all nodes Both distributed and centralized algorithms can be properly designed so that alternate routing is obtained However both have limitations inparticular distributed algorithms 7 1 Network Analysis Corporation suffer the limitation of being local i e routing decision is based r»n local traffic information or on global but generally out of date traffic information centralized routing algorithms can achieve a better global utilization of alternate routes but cannot react rapidly enough to traffic changes In the following we present some new concepts for the design of efficient high bandwidth routing algorithms which combine desirable characteristics of both approaches 3 SOURCE AND DESTINATION ROUTING ALGORITHMS Intermediate solutions between distributed and centralized routing scheme are represented by the source and the destination routing algorithms In the two latter algorithms each node collects traffic information from all the other nodes Using such information and having the global knowledge of network topology and channel capacities the node evaluates appropriate equivalent lengths for all the links in the network Next in the source algorithm each node evaluates all shortest routes according to the above lengths from itself as a source to all the other nodes in the destination algorithm each node evaluates all shortest routes from all the other nodes to itself as a destination Alternatively instead of shortest routes maximal residual capacity routes can be determined At the end of the shortest route computation each node propagates into the network the routing information in the form of a routing vector Efficient alternate routing is obtained by repeating such shortest route computations at a frequency that will depend on network saturation and presence of particular high bandwidth requirements After each computation naw routes 7 2 are obtained and the traffic is optimally distributed between new and preexisting routes As an example assume that a high bandwidth requirement arises from source S to destination D If source routing is used the source node attempts to accomodate such a requirement on the S D route or routes presently available If there is no sufficient excess capacity on such routes the source computes the new shortest rovte from 5 to D and accomodates additional traffic Shortest route computations are repeated until the requirement is entirely accomodated or there are not more residual capacity routes between S and D In either case the source algorithm provides a smooth flow control on the input rate of the high bandwidth requirement 4 COMPUTATIONAL CONSIDERATIONS In the sequel the question of the feasibility of source and destination routing implementations on minicomputers like those used in ARPANET is addressed To answer such a question the amount of computation and of memory ppace required by the algorithms is investigated In particular the two routines Shortest Route and Flow Assignment are described which are the backbone of both algorithms and account for most of the execution time and memory space requirement 4 1 SHORTEST ROUTE ROUTINE As mentioned before the source routing algorithm re- quires the computation of all shortest routes from the given source to all the remaining nodes conversely the destination routing algorithm requires the computation of all shortest routes from all nodes to the given destination In both cases 7 3 a modified Dijkstra's Algorithm is used which applies Floyd's Treesort Algorithm for the sorting of the minimum distance node at each step The computational complexity required to find all shortest routes is theoretically bounded by NN lg2NN NA for comparison operations and by NA for addition operations where NN is the number of nodes NA the number of links In practical cases such as ARPANET the computational complexity with respect to comparison operations can be further reduced by treating the 2 and 3 degree nodes separately and it approaches the lower bound NA The modified Dijkstra's Algorithm for the computation of shortest routes from source S to the other nodes is described below A similar algorithm can be used to find shortest routes from all nodes to a given destination Before introducing the algorithm a few definitions are necessary 4 1 1 HEAP A list of m 2 -1 numbers n n2k_ can be identified with a rooted binary tree with k levels where n is at the root n2 and n3 are at the next level and in general nJ- and n2i - at level i 1 are connected to n at level i In figure 1 this mapping is illustrated for k 4 Network Analysis Corporation The list L binary tree associated k n n Vi l 2 -1 heap is the minimum of 4 1 2 n n2k_ or equivalently the with it is called a heap ifn n_ and i e the element at the top of the the list DATA STRUCTURE DIS I NN is the vector of shortest distances from S to each node I and constitutes the heap of the molified Dijkstra's Algorithm D IJ IJ 1 NA is the vector of link lengths Assuming that the index IJ corresponds to the link I J then D IJ is the length of link I J NODE K K 1 NN is the vector of pointers from heap to list of nodes PRE I 1 1 NN is the vector of predecessor In particular PRE I is the node preceding I in the shortest route from S to I 4 1 3 Step 0 Modified Dijkstra's Algorithm Assume source node S is labeled as node 1 Initialize NODE I DIS I NODE 1 DIS 1 Step 1 I °° 1 0 jv j 2 _NN Scan the top node in the heap Let I NODE 1 For any unscanned node J adjacent to node I 7 5 • wr i # J-WUl 313 UUf yUfUllLffl If DIS J DIS I D IJ then Step 2 DIS J DIS I D IJ PRE J I Do a treesort on the heap DIS Remove the top node which is now scanned If K is the lowest DIS NODE K oo let index in the heap such that NODE 1 NODE K NODE K 0 Step 3 Do a treesort If DIS NODE 1 °° Stop Otherwise go to 1 At the end of the algorithm DIS I represents the shortest distance from S to I for all I PRE I represents the predecessor of I in the shortest route from S to I Notice that some minor modifications to the algorithm allow maximum residual capacity paths to be found instead of shortest paths 7or example in a maximum residual capacity algorithm DIS I represents the residual capacity on the best path to node I the top of the heap is the node which has currently the maximum residual capacity the test in Step 1 becomes DIS J min DIS I RS IJ where RS IJ is the residual capacity of link I J 7 6 4 1 4 AMOUNT OF COMPUTATION REQUIRED BY DIJKSTRA' S ALGORITHM The time consuming steps of the algorithm are Step 1 and Step 2 If k is assumed to be the number of unscanned nodes adjacent to the node presently scanned and NX the total number of labeled and unscanned nodes typically NX NN then • Step 1 requires k additions _ k lg2NX-2 comparisons k lg2NN-l interchanges • Step 2 requires 21g_NN-2 comparisons lg2NN-l interchanges Recalling that Step 1 and Step 2 are executed at most NN times the upperbound on computational complexity is proportional to NN lg NN Further computational reduction is obtained if the network contains several nodes of degree _ 3 in such case it is possible to make the upperbound proportional to k1 NN'lg2NN' k2 NN k3NA where NN' is the number of nodes of degree 3 and NN is the number of remaining nodes 4 1 5 FLOW ASSIGNMENT ROUTINE Let the NN-vector REQ I 1 1 NN contain the flow requirements from S to all other nodes such a vector is evaluated node S Let us assume that the nodes are relabeled in the order they were removed from the heap i e in the orde ol increasing DIS I Let the NA-vector FLOW K K-l Nä contain the link flows obtained by assigning flow requirements to shortest route flows 7 7 Network Analysis orporaiiun Step 0 Initially FLOW I 0 V 1 1 NA NL NN Step i NF PRE NL FLOW FL REQ NL where FL is the index of link NL FL REQ NF REQ ' NF REQ NL Step 2 If NL EQ l stop NL NL-1 Go to 1 The amount of computation required by the flow assignment is linear in NN 4 1 6 STORAGE REQUIREMENT The following arrays are required for the shortest route evaluation 1 NN-vector with node degrees 2 NN-vector with node status nodes up or down 3 NA-vector with link capacities 4 NA-vector with link flows 5 NA-vector with link lengths 6 KA-vector with line status lines up or down 7 NA-vector with adjacent nodes 8 NN-vector with pointers from the list of nodes to the vector of adjacent nodes 9 NN-vector with shortest distances 10 NN-vector of pointers to the heap 11 NN-vector of pointers from the heap 7 8 Network Analysis Corporation In addition the following arrays are required for the flow assignment 13 NN-vector with flow requirement from source S to all other nodes 14 NN-vector with the list of nodes in the order they were removed from the top of the heap 15 NA-vector with new link flows 4 1 7 ROUTING TRAFFIC OVERHEAD Routing traffic corresponds to 1 Line traffic information which must be transmitted to each node so that line lenghts can be evaluated and shortest routes computed 2 routing information which is based on shortest route computation and is transmitted from the source or the destination node to all other nodes Line Traffic Information each node evaluates average flows on its output channels and distributes such information to all other nodes in the network using a propagation scheme Routing Information each source or destination transmits the routing vector to all other nodes using a propagation scheme 5 CONCLUSION AND FUTURE RESEARCH Source and destination routing algorithms are conceptually very simple and can accomplish an efficient high bandwidth utilization Their computational requirements are within the capability of minicomputers of the size of an ARPANET IMP Further research is required to develop a routing algorithm which implements the new concepts 7 9 «WSSStfSS ii Network Analysis Corporation A SYSTEM FOR LARGE SCALE NETWORK COMPUTATIONS - PART 1 1 INTRODUCTION Extensive experience in the design and implementation of sophisticated algorithms for network analysis applications has established the need for improved computational approaches to large scale network design While rapid advances have been made in algorithm design using methods such as computational complexity analysis non-linear programming theory and decomposition techniques the method cf computation has remained relatively static Remote job entry to a single large scale scientific computer in a batch mode has been the predominant approach to large network problems This mode is very efficient for performinr the algorithmic computations but unfortunately it is inadequate for human use Consequently the effectiveness of the remote job entry approach is limited Time sharing on the other hand has many attractive user oriented features but it does not offer an acceptable alternative because extensive network computations cannot be carried oat on a time shared basis Developments in parallel processing distributed computing programming language theory data structure design and interactive graphics offer many opportunities to improve nee work computations The application of these developments to practical large scale network computations has only recently begun To collect and focus NAC's efforts in this area the Laboratory for Large Scale Network Computations was established to study and develop mechanisms for carrying out computations for large scale network applications A facility for such computations consists of computer hardware systems and communication software and the software implementing network algorithms Section 2 describes the hardware resources of the laboratory and Section 3 details the progress and plans for systems and communication software Specific large scale network algorithms are described in the other chapters of this report 8 1 ■ '•-''• ■' ■ ■■ ' ■ ' Network Analysis Corporation HARDWARE RESOURCES FOR NETWORK COMPUTATIONS 2 1 NAC COMPUTER CENTER The NAC computer center is bui t around three remote job entry terminals now used exclusively for access to CDC-6600 computers at various sites Two of the terminals are CDC-200 User Terminals boch equipped with a medium speed card reader and line printer and a hardwired controller The third terminal is a Un tech UT-1 intelligent terminal built around a Data General 1220 Nova computer with high speed card reader line printer and 7 track tape drive In addition there are two large CalComp flat-bed plotters one of which is connected online to one of the 200 User Terminals The other is capable of being driven in either an online or an ofrline mode through the tape drive by the Unitech System Additional computational equipment is in the laboratory itself 2 2 LABORATORY HARDWARE The first equipment for the laboratory was delivered in the fall of 1972 and consisted of 1 An IMLAC PDF-ID programmable graphics display unit with 8K of memory long vector hardware cassette tape unit and a mouse for graphic interactions 2 A Texas Instruments 720 Silent Terminal and 3 An Andersen-Jacobson combination 103 type modem and acoustic coupler In slightly over a year two Infoton terminals have been added and leased lire connections to the ARPANET have been made to Tip's at CCA in Boston and at the National Bureau of Standards in 8 2 Washington In July 1973 NAC began an experiment to provide low cost terminal access to the ARPANET even though the nearest TIP is over 200 miles away from NAC's facilities In this experiment several terminals were multiplexed onto a single voice grade line Presently the three CRT terminals operating at 1200 bps and the T I 720 a 300 bps are multiplexed onto one voice arade line using a Bell 4800 bps modem Since this is a new way of utilizing the ARPANET the next section is devoted to describing in some detail our experiences in connecting a multiplexed line into the net 2 3 MULTIPLEXED ACCESS TO THE ARPANET TIP Because NAC is distant from any ARPANET TIP site terminal access through conventional dial-up or multiple leased lines to serve a number of users at NAC is expensive For example in a single month of dial-up useage when NAC first began using ARPANET dial-up communication charges were over 50% of total computation cost To reduce communication costs NAC was first connected to a TIP via a leased line by means of a Bell 103A2 modem with a ring circuit connection operating at a 300 baud maximum This initial implementation was chosen because it was the only leased line configuration that had been connected to a TIP by late 1972 As ARPANET usaye yrew the following sequence of steps was planned to reduce network access costs 1 A remote terminal was connected to the TIP without the complications of a ring-circuit 2 Higher speed lines for use with CRT terminals could be utilized with appropriate modems 3 To serve the users at NAC lines could be multiplexed without the need for additional equipment beyond the multiplexers and appropriate modems 8 3 ■ » Network Analysis Corporation A survey showed that none of the above steps had been attempted or implemented elsewhere Hence to increase the probability of success the NAC mplementation was sequential The first step was to determine whether higher speed leased lines could operate with the TIP under a simple connection strategy A 1200 baud leased line was connected from NAC to the CCA-TIP with Bell 202R modems without the added complications of the multiplexer Before this time the 202R had not operated well with the TIP for other users but this stage of the implementation went smoothly A 4800 baud line with Bell 208A Dataphone 4800 modems was then installed After some difficulties in testing it due to voltage reductions in the New York area the line was declared operational A pair of T-4 Timeplex multiplexers were then connected at NAC and at the CCA-TIP site Initial tests proved that the multiplexer line configuration was successful the TIP recognizing each line uniquely at the speeds required Two problems were uncovered at this time 1 The multiplexer was equipped with cards which require parity on data received 2 The multiplexer was equipped to operate with attached modems rather than terminals The first problem caused certain ASCII characters to be acknowledged by the T-4 as control information This was corrected by ordering different high speed cards which supplied parity for the internal operations of the T-4 and then removed the parity again when outputting the data The second problem has still not been satisfactorily settled although patches have been uade to temporarily circumvent the difficulty Apparently terminals connected directly to the T-4 do not supply all 8 4 Network Analysis Corporation of the necessary EIA signals which recent TIP versions TIP'S 315 and 316 now require e g carrier detect After some experimenting NAC found that by patching EIA signals data-terminal-ready and request-to-send together the system operated successfully The multiplexed line configuration is highly cost effective Cost for the line from NAC to CCA have two components 1 The Inter-Exchange Connection IXC charge from NAC to the Telpak connection approximately 8 miles is $26 50 month 2 There is a Telpak charge of $0 50 mile month for the remaining air miles to CCA The equipment charges at both sites include the price of the modem and additional equipment at the specified site and a charge for the equipment at the IXC Telpak connection which is included in the equipment charge for one of the sites The 103 A2 modem also had alternate viice capability Table 1 shows a breakdown in cost per modem The total cost is the monthly cost for the modems and lines the Telpak charges are conservatively computed assuming 300 air miles from Nassau County New York to Boston Massachusetts The cost of supporting the Timeplex T-4 multiplexer Bell 208A modem and leased line configuration is $522 90 monthly for the line plus a $1 610 00 purchase price for each T-4 unit Without the multiplexer three lines with 202R modems and one line with 103 A modems would cost $1 193 10 per month Thus within six months both multiplexers have been completely paid for with the savings generated 8 5 Ne work Analysis Corporation 3 SOFTWARE FOR LARGE SCALE NETWORK COMPUTATIONS 3 1 A PROTOTYPE •- THE NETWORK RELIABILITY ANALYZER The first effort a developing improved large scale network software was aimed at a typical applied network problem-network reliability analysis The system designed was used as a prototype User experience was used to suggest improved computational techniques for large scale network problems and to evaluate the implementation of the conjectured improvements The abstract problem of network reliability analysis is to calculate the unknown reliability of a network given the reliaiblities of its nodes and links The applied problem was the reliability analysis of data communication networks in particular the analysis of ARPANET In the original topological design of the ARPANET Roberts and Wessler 1970 Frank et al 1970 network reliability was assured by requiring that at least two communication computers or telephone lines must fail before two functioning computers are disconnected from one another As data was collected on the availability of lines and IMP'S the availability of the network became a parameter that was not only important but was also computable In the first phase of the research a very flexible simulation method was developed for performing this calculation Van Slyke and Frank 1972 a Van Slyke and Frank 1972 b Since many samples nust be taken in a simulation model to achieve a small variance it is essential to make the sample determination as efficiently as possible To do this computational complexity analysis was brought to bear Lawler 1971 Miller and Thatcher 1972 First it was discovered that the sample determination is essentially equivalent to finding a minimum spanning tree on the network In Kershenbaum and Van Slyke 1972 a careful analysis of the computational complexity of minimum spanning tree algorithms was carried out resulting in substantial improvements over traditional algorithms Generalizations of these techniques of computational complexity analysis are being applied to other important areas of network analysis 8 6 Network Analysis Corporation The result of this phase of the work was a very flexible and efficient computer algorithm written for remote job entry to a CDC-6600 computer Much useful information was developed using this code It was found that for networks the size of the current ARPANFT the reliability implied by requiring at least two elements to fail before any disconnection yielded adequate available for the net although it was also discovered that for larger nets this approach was not adequate Reconfigurations of ARPANFT which dramatically increased reliability at very little cost were discovered usina the program Variants of the program were applied to a wide variety of communication networks including centralized networks and command and control networks Frank 1974 At this point efforts to more effectively use computational resources for solving network reliability problems were intensified The first experiment along these lines was to make the program interactive so that analyzing the reliability of a sequence of variants of a basic configuration could be carried out conveniently The first crude version of an interactive network analyzer was demonstrated at the International Conference on Computer Communication in Washington D C October 24-26 1972 The program was implemented on an IMLAC PDS-1D graphics display unit working with a PDP-10 with a TENEX Operating System Communication was through the ARPANET The user could type in a network of his chosing or start with a very small version of the ARPANET having 10 nodes He could then edit the network by adding or deleting links He could specify node and link failure probabilities either by assigning a common value to each node and another common value to each link or by assigning different values to each element Finally a random number seed the number of samples and the range of variation for the probcbilities had to be specified After the simulation was completed the user had a choice of tabular output graphical output or both The program then displayed the network 8 7 Network Analysis Corporation analyzed so that further modifications could be made and another simulation carried out The program had the capability simultaneously displaying the reliability curves resulting from three different simulations Thus one could easily compare the reliability of networks where reliabilities and or topology were varied This first version was well received at the conference It was also considerably easier to use than the previous remote job entry version for demonstration problems However there were still several serious inadequacies 1 The input was required to be in rather rigid format making it almost impossible to enter any but the smallest of networks 2 If any errors were made in entering the data the program had to be restarted from the beginning 3 If any portion of the network was modified the entire display had to be redrawn and retransmitted from the PDP-10 4 Nodes could not be added or deleted from the network 5 The program could only be operated on the IMLAC PDP-10 hardware configuration 6 The display of a net could not be modified to make it clearer 7 Large networks had to be entered by the programmer and could not be saved Network topologies could not be read in from a previously created file 8 8 8 Operating the program was slow because of the necessity for elementary operations for use by beginners of the system 9 IJodes ai d links could only be differentiated by sequential numbers assigned by the program rather than by labels or by varying symbols 10 Since the simulation was being carried out on a timeshared computer and the computation was extensive it was only possible to analyze small networks usinq a small number of samples For example for the demonstrations at ICCC even for 10 node networks and 100 samples the delav due to competition with other user ■ of the time sharing system could run to several minutes when the computer was heavily loaded 11 The graphic display is vulnerable to line noise since it is connected to the time sharing computer by an asynchronous line with no error checking or facilities for retransmission Moreover the display vector coimtands are usually given relative to the end of the previous vector Thus if noise causes a translation of one vector it also causes a translation of all of the vectors dependent on it 12 Very large networks could not be displayed even if they could be read in - see 1 2 6 because of limitations on display screen size It is noteworthy that all of the above twelve difficulties could occur in any application of standard computational systems to large scale network computations In the next phase of research 8 9 Network Analysis Corporation prototype computer utilities were developed which not only made the network reliability analyzer more effective but which can also be used for better large scale network computations in general This effort culminated in early Summer 1973 with the second version of an interactive network reliability analyzer f'any but not all of the twelve difficulties of the earlier version were eliminated by the creation of several network analysis utilities Free for Ttat routines -were created opportunities for remodifying data without restarting were inserted modification of the pictorial representation of a network could be made without completely redrawing the network nodes could now be added deleted and moved on the display a teletype version of the program was installed on the ARPANET for other users who did not necessarily have an IMLAC This program was used successfully by at least one user at SRI networks could be read from files and after computation large networks could be saved on files automatically and nodes could be characterized by alphanumeric lavels as well as by differing symbols e g diamonds boxes triangles and circles In addition a mouse capability for directly interacting with the graphic representation of a network was introduced Work currently in progress is to use distributed computing to combine the advantage of the raw computing power of basically remote job entry computers such as the CDC-6600 and the IBM-360 91 with the flexibility and ease of use of interactive computing on time sharing computers The basic configuration is to use a TTY CRT or graphics terminal together with a time sharing computer like the PDP-10 TENEX system for entering data and generating a remote job entry file for transmission to a large scale scientific machine which does the computation The output is then returned to the time sharing computer for examination Two network analysis programs a program for the topological design of regional high density terminal oriented TIP 8 10 Network Analysis Corporation networks and a program for traffic routing on distributed communication networks have been used in this manner However the programs were basically straightforward remote iob entry codes without the interactive features developed for the network reliability analyzer The next version of the network rejiability analyzer which will be completed shortly will combine the desirable features of the interactive version and the computational efficiencies of the first remote job entry version 3 2 A SOFTWARE TASK FORCE A review of the computation reauirements for large network problems based on years of extensive overall experience in the area or large scale network computations and on the particular experience gained in building the various forms of the network reliability analyzer was begun in the Summer of 1973 Initial conclusions were that it was now possible to design a general computation system for large network problems To this end in July of 1973 a task force was appointed to design a computation system that would exploit recent advances in distributed computation interactive graphics programming language theory theory of data structures and other modern computational resources for the more effective solution of large scale network problems Included in the mandate for the group were the following requirements and engineering constraints 1 Ease of Use The system should be equally accessible to users with little programming or network analysis experience and to experts This is to be accomplished by a Several levels of documentation ranging from one or two sheet explanations of the most useful and basic aspects of the system up to full documentation of the system which should suffice for expert programmers to recreate the entire system 8 11 % IVZlwvrn rwiviyjt ww w b On line interactive aides which can inform users in real time how to use the system and c Intelligently chosen defaults for options which will allow users to ignore the more erudite features of the system which they may not need 2 Efficiency in the use of a Communication Networks b Computer time in execution of computing bounded programs c User time and patience 3 Capacity The system should be capable of handling large scale networks 4 Machine Independence In order to take advantage of resource sharing on the ARPANET the system with slight and well defined modifications should run on the major computers of the network 5 Flexibility It is most important that the system be developed in stages and that the result of each stage be useful and applicable without the need to wait for the system to be completed Required of the group in addition to a system design was a schedule of implementation which would be gradually carried out with the most useful features implemented first so that practical 8 12 Network Analysis corporation and useful results would be apparent from the beginning The design and the schedule of implementation should be motivated by reouirements generated in practice based on the experience gained by the network reliability analyser 3 3 PRELIMINARY RECOMMENDATIONS AND INITIAL IMPLEMENTATION By the late fall of 1973 a consensus was beginning to emerge on the general outline of a large scale network computation system It would consist of two languages - a Network Editing Language and a Network Language The Network Language in turn has two parts - a Network Structure Language and a Network Programming Language As network problems get larger necessary algorithmic calculations become more complicated as expected However problems of data management grow much more dramatically and often become the major source of difficulty Errors in input become inevitable while error detection and correction become much more difficult In extreme cases extensive computations are often rerun many times before trivial input errors with obvious effects on the output can be corrected Thus it was decided that the initial emphasis should be put en the Network Editing Language Conceptually the Network Editing Language is very much like a text editor except that the domain of application is networks rather than text The main complications come form the variety of ways the network being modified can be displayed to the user The network structure can be fed back to the user as a list of nodes links and properties on a TTY of CRT alphanumeric display or graphically on an interactive display device or flat-bed plotter Text editors must often deal with more text than can be displayed at once Equivalently the Network Editor must deal with networks that are too large to be displayed in their entirety on a graphics terminal Consequently windowing and other graphics display techniques must be built into the editor In the next section the design of the first version of the 8 13 Network Analysis Corporation » • Network Editor is given The Network Language is in a more rudimentary state As mentioned before it consists of two sub-languages a Network Programming Language and a Network Structure Language The Network Programming Language will be an extension of FORTRAN which admits network structures and operators resembling for example FGRAAL Rheinboldt et al 1972 Most such languages are ineffective in an applicaitons environment because of their relatively rigid data structure Either the structure is too complex so that the program runs inefficiently or it is too simple in which case many applications do not fit gracefully to the language The Network Structure Language which can be thouqht of as an extension to the declarative statements in FORTRAN allows one to use exact''y that data structure which is appropriate to his problem 4 THE NETWORK EDITING LANGUAGE The Network Editing Language provides a set of commands by which the user can modify a network data structure The network data base consists of nodes links and properties corresponding to nodes and links The editing language must supply commands to add and delete nodes and links and assign values to their properties It also supplies the necessary prompts to the user when input is required 4 1 DESIGN Three factors must be considered in the design of the command language 1 simplicity 2 consistencv and 3 economy All are closely interconnected and the command syntax must be written in such a way as to optimize ec»ch factor relative to the others The goal is to minimize the number of commands define each on the same syntactical base and liirit the amount of input required for each command Special features and options can be added for experienced users but the basic command structure should be maintained 8 14 Vf tworn Analysis lA rporwvn 4 1 1 Command Syntax Commands are defined to he any input or sequence of inputs that modity the user data base A command consists of two parts 1 the Verb and 2 the Agruments The verb is a single character which will activate a process Requiring the verb to appear before the arguments has two advantages 1 Commands are easier to process and allow a variety of argument syntax and 2 The program is able to respond to each succeeding input element in an appropriate manner and prompt the user if data is not entered The arguments are '-he necessary control information and data for editor use An example of a command is 'A N 5' where 'A1 is the verb to ADD snd ' N' and '5' are the arguments specifying Modes and tns quantity 5 This command would add 5 nodes into the data base 4 1 2 Command Structure Commands must be simple enough for a new user to learn and concise enough to allow experienced users to omit reduntant control information For example consider the command to assign a value to a node property in the network The basic command allows the user to enter a property identifier the pid and the value to be assigned Tor a specified node the pval Assume that nodes have 2 properties their TYPE pid T and LABEL pid L The basic command allows the user to assign a property to a node noc- 5 for example S N 5 T 1 S N 5 L N05 a 15 Network Analysis corporation while the concise command allows listing the pid pval pairs S N 5 T 1 L N05 Even the second form is still verbose if these properties have to be assigned to a large number of nodes For this a special command M for MACRO provides very concise commands for frequently performed operations on large data bases In the sections to follow commands v ill be introduced on the most basic level and additional features are discussed 4 2 NOTATION The following symbols and notations are used in command des- criptions % $ carriage return escape # # pid pval N comma prompt continuation prompt information enclosed in brackets is supplied by program blank or space positive integer property identifier property value node label for node i N N node label pair defining link N N delimits a repeated field in a macro command 8 16 4 2 1 Delimiters The concept of a field is important to the command The verb and each of its arguments in a command is contained in a field The field is delimited by a comma a blank or a carriage return which terminates the command Taking the example from above S II 5 T 1 L N05% seven fields are specified the first is the verb and the rest are arguments The final argument is delimited by the carriage return In the command descriptions the comma will be used to delimit all fields except the last one A blank can replace the comma a string of blanks is considered as one or can flank the comma for legibility The blank cannot however replace a comma before a carriage return which specifies continuation of an argument list Another set of delimiters will he discussed in Section 4 6 1 These will involve additional symbols which will not delimit the fields as such but rather serve as guides for the user on inputting data 4 3 COMMANDS BASIC LEVEL At the basic level we are interested in supplying commands to do what is minimally required to enter a network definition These commands are more suited to editing an existing data base hut could be used to enter a small network of say 10 nodes and 20 links each with a few properties Primarily they are presented to give the flavor of command structure and description techniques 8 17 - i Network Analysis Corporation 4 3 1 Add Command - 'A' The 'A' command adds nodes and l-aks to the network The nodes are assigned default labels as they are added by which the user can reference that node in later commands A H #% will add '#' nodes to network A L N N N N N N % 1 D 1 x 1 l 2 2 k - k will add links N lx N jJx x l k k lto network 4 3 2 Delete Command - 'D' The 'D' command deletes previously defined nodes and links from the network D N N1 N2 Nk % will delete nodes N N» N k 1 Note that when a node is deleted any links indicent to that node are also deleted D L N N N N % 1 X 1 - l k Jk will delete links N y x N x 1 J x 8 18 Network Analysis Corporation 4 3 3 Set Command - 'S' Now that the network has been defined the user can assign values to those pioperties needed by the program Assume that nodes have a property TYPE pid T and links have a property LENGTH pid L To assi-n a tyoe to note 5 enter S N 5 T 2 % In general S N N pid pval % for nodes S L N N pid pval % for links X l D l To set the value of every node pid to the same pval enter S A N pid pval % and for links S A L pid pval % 4 3 4 Summary We now have a set of commands to allow the user to enter node and link definitions and assign values to their properties The keying in of input is considerable In the next section we will introduce new commands to perform more actions with less input 8 19 Network Analysis Cor toration 4 4 COMMANDS CONCISE LEVEL This section will present commands or extensions of previously defined commands which can be used to enter the network definition with less effort 4 4 1 Continuation of Argument List In commands which accepted a list as part of the arguments the list was terminated by the first carriage return By delimiting the last field prior to that carriage return with a comma the program will read in another line of input and take it as a continuation of the argument list i or example if nodes had a few properties then many nodes could be assigned values for their properties in a single command S N N1# pidj pval pid2 pval2 % N2 pid3 pval3 pid4 pval4 % Note the comma before the carriage return in the first line which is required and the subsequent double prompt in line 2 In the next section we see how a macro can remove the unnecessary pid's when they are the same for each node 4 4 2 Add Set Command - 'A S' Since most programs require properties associated with the nodes and link a reasonable time to enter the values of those properties corresponding to that node or link is when it is initially defined Thus a new command is introduced which does two things 8 20 1 It will add the element being described if it does not exist and 2 It will assign the given values to that element For nodes entering A S N N1# picL pval i 0 will add Node N with property values pval if J does not already exist Similarly for links A S L KL N pidk pvalfc k _ 0 will add link N N if it does not alreadv exist J 1 l If the element does exist it will be considered or error since this is an ADD command 1 4 4 3 Summary The amount of control information is now only a percentage of the total amount of data keyed in Even this amount is much too large for a 1 000 node networks Although it's impossible to completely eliminate the control information we can reduce it considerably by using macros for frequently performed operations Macros and variable length property values are the subject of the next section 8 21 Network Analysis Corporation 4 5 COMMANDS EXPERIENCED USER LEVEL For networks with nodes or links which all have the same properties and values which must be assigned to the properties it would be ideal to add the node assign the values and omit all control information This is done by the MACRO command For some properties the value assigned might be a ation of two or more values For example the LOCATION of a might be its longitude and latitude Longitude and Latitude properties of LOCATION not of the node so that in response SET of property LOCATION for a node the pval becomes a pair latitude which must now be added 4 5 1 combinnode are to a longitude Macro Command - 'M' In an effort to eliminate control information the Macro command supplies a command skeleton with slots for required input A macro is constructed by preceding a command by 'M' The program will now save this input and all further input will be controlled by this skeleton or format Whenever a ' ' is encountered a value is taken from the input and the command processing continues For example suppose we wich to enter a large number of nodes with the following properties 1 DEGREE pid D 2 X-COOR pid X 3 Y-COOR pid y 8 22 Sei warb Analysis Corporation We can use the Add Set command K 1 M A s M n y v Macro ready 1 1 120 150 2 1 135 173 % 7 2 200 153 % 88 2 350 90 % tZ % The tZ control - Z terminates the macro and returns to the command mode The macro defined above will input the lines following as if the values were entered with all the necessary control information A S N 1 D 1 X 120 Y 150 1 A S N 2 D 1 X 135 Y i % An attempt must be made to keep the range of the macro restricted or else the system becomes unduly complex 8 23 Network Analysis Corporation 4 5 2 Multiple 'Pvals' In some applications a property may be considered as a group of values For instance if we assume nodes to have properties X-COOR X and Y-COOR Y the assignment command has two control arguments S N N X pval Y pval This could be extended to a Z-COOR Therefore one way to reduce the control information is to group the three or more properties under one property say POSITION P S N N P pval pval pval This is a possible1 extension of the language However the macro feature should be able to handle this case whenever information of this type is to be entered S N X Y Z If editing must be done on these properties they can be entered individually rather than grouped 4 5 3 Argument List The properties entered on a line of input may vary as to length i e there may be a property which is a list of pvals Suppose we consider nodes to have the property of the number of terminals K connected to it and a list of the terminals T S N 14 K 3 T Tl T T2 T T3 specifies that node 14 has 3 terminals Tl T2 T3 connected to it 8 24 Network Anah Corporation If this command is incorporated as a macro a question arises as to how many slots to leave in the list Tor rhis application we introduce the list element in an araument list in a macro • M s N K T where the T is the list element to be repeated ' N' time under program control 4 6 OTHER DESIGN CONSIDERATIONS This report has introduced the basic command syntax and the commands supplied to edit and initialize a network data base Other areas in this editing lanquage must still be considered and the following sections we discuss a few of them 4 6 1 Input Delimiters To allow input to be more readable to the user t e following specifications are proposed 1 Parentheses can delimit a node pair defining a link as N N i D 2 A pid pval pair can he entered pid pval 3 A verb can be followed bv a slash as A N 5 % to highlight the 'A' as a verb Difficulties arise v hen programming such a syntactical scheme in a language such as FORTRAN if the delimiters are permitted to be entered optionallv Thus as a matter of policy these symbols will simply be considered blanks and become part of the delimiter separating the fields it lies between 8 25 Network Analysis Corporation 4 6 2 Input Output Commands Commands must be provided to permit the user to list on the teletype the network definition or cause it to be displayed or plotted and to save versions of the data base for subsequent sessions This also implies a command to input the information saved from a previous session 4 6 3 Error Detection and Handling Three types of errors can occur while inputting information 1 the user may mis-key a character e g hitting a ' ' instead of a M' 2 the user may enter an invalid command and 3 the user may enter data which the program determines invalid The first case is the simplest and requires a special character such as tA to delete the most recently entered character The second error condition occurs when the program is expecting a certain input such as the number of nodes to be added or a set of inputs such as 'N' or 'L' for a Delete command The third condition is similar to the second in that the program detects an error which is found to be inconsistent with the data already available It is not clear in the latter case whether the input on which the error was detected or previously entered information is the cause of the error Procedures for handling these errors will be developed as a result of user experience and misadventures 4 6 4 Prompts to User When the program is expecting input there should be a short prompt available to be displayed to the user when the is unsure as to what is expected This is especially desirable for a new user of the system but is always an aid when input has become messy or the program must be continued 8 26 Network Analysis Corporation CHAPTER 9 PACKET RADIO SYSTEM - NETWORK CONSIDERATIONS 1 INTRODUCTION The Packet Radio System is a broadcast data network extend- ing a point-to-point packet communication system such as ARPANET Roberts 1973 to provide local collection and distribution of data over large geographical areas Since the system is wireless it will be especially effective for mobile devices devices for which the peak data rate requirements are much higher than average requirements and devices for which hardwire connections are not feasible The system is designed to be economical reliable secure and conservative of spectrum The properties and implementation of a Packet Radio System are being studied under the direct guidance of ARPA by Collins Radio Corporation Network Analysis Corporation Stanford Research Institute the University of Hawaii and the University of California at Los Angeles An extensive discussion of the uses and need for the Packet Radio System is given by the project director R Kahn Kahn 1974 In this chapter we discuss the network aspects of the Packet Radio System which must be taken into account in order to make the system workable Any network consists of nodes and links In the Packet Radio System nodes correspond to communication devices and links to transmission on the channel These aspects are discussed in Sections 3 and 4 The geographic layout of the netvork is discussed in Section 5 9 1 Network Analysis Corporation 2 NETWORK OVERVIEW There are three basic functional components of the Packet Radio System the Packet Radio Terminal the Packet Radio Station and the Packet Radio Repeater See Figure 1 Packet Radio Terminals will be of various types including personal digital terminals TTY-like devices unattended sensors small computers display printers and position location devices The Packet Radio Station is the interface component between the broadcast system and the point-to-point network It will have broadcast channels into the Packet Radio System and will have link channels into the point-to-point network In addition it will perform accounting buffering directory and routing functions for the overall system The basic function of the Packet Radio Repeater is to extend the effective range of the terminals and the stations especially in remote areas of low traffic and thereby increase the average ratio of terminals to stations A more detailed discussion of the network h rdware functions can be found in Section 3 The devices repeaters stations and terminals of the Packet Radio System communicate in a broadcast mode using the Aloha random access method Abramson 1970 which is suitable 9 2 re e o o rt o a o •M c o re J o -3 -a rt re Network Analysis Corporation 4 C C re cu o -• a re o c c re x u a •■H c o u en 0i •-H a H UJ u l 0 l 0 g 3 9 3 0 © ■ ■ Network Analysis Corporation for terminals Roberts 1972 a that i are mobile so that a broadcasting mode is necessary ii are located in remote or hostile locations where hardwire connections are infeasible iii have a high ratio of peak bandwidth to average bandwidth requirements because the Aloha method allows the dynamic allocation of channel capacitv without centralized control or iv require little communication bandwidth so that hardwire connections are uneconomical The channel characteristics of the Packet Radio System are described more fully in Section IV Stations will be allocated on the basis of traffic Thus to first approximation we can think of partitioning the area to be covered e g the United States into regions of equal traffic and allocate one station for each region In regions of low traffic density the station may not be in line of sight of all the terminals in the region hence repeaters are used to relay the traffic to the station Thus repeater correspond to a geographical partition of the area into sections small enough so that each terminal can communicate with a repeater and be relayed by it to a station In areas of high traffic such as urban areas repeaters may not be needed in fact the problem may be that a station 9 4 IVtriWUiK rwiuiv-Hj vui vif« can communicate with more terminals than it can handle Broadcast of data in urban areas is also complicated by extreme multipath interference Turin 1972 The rapidly expanding Cable Television CATV Systems within urban areas offer an attractive alternative to over-the-air broadcasting except for mobile users who must use broadcast techniques The same general Packet Radio concept can be applied to Packet Communication on CATV systems This approach is explored in detail in NAC 1974 b As a gross estimate of the size of such a system suppose the 3 536 855 square miles of land area in the United States are to be covered Then if the average useful area that a re2 peater can cover is TTIO square miles we would need approximately 11 258 repeaters In Table 1 a sample traffic distribution is given based on one due to L Roberts 1972 b We assume that the number of the various types of terminals is proportional to population Thus in column b of Table 1 we give the relative number of arious terminal types per N people where N is an arbitrary constant of proportionality In the table reasonable assumptions relative to the numbers of the different devices are made For example there are twice as many 100 TTY's and personal radios as position locators 501 per N people Columns a through h specify the characteristics of the devices 9 5 Columns i and j give Network Analysis Corporation m O oil«« IM x 3 2 o o CM WHi- CM •H oe in o m m ■ m 01 m o» cd U «i UH v« 44 0 44 M x U 0 • © Kl at o eo -1 O o 3 o rm ♦ m 3«ljJ O m CM CM O co t« m o m «» o d h X in 4J 0 »J Ö «- O -ri X -H CM H ea A4» o« • m y 'S a 0 0 StJ c w 0 -H M K«l«l V Üf U «X'Hjj «JO 43 0 ■ •«t «9 CM 0 0 00 0 in 0 O o o o o in in t o o 00 m 1— CM z o O o o o o o o o Kl in •si «ft ° c 3 o o 1 1 u t—I o a o o m o o m o m o -3 s fg •H c 0 w Kl « 10 o Sin t o CD C • 3-rt-g 00 g rH 0 0 ■ p 43 OA Oh c 0 0 O -rt a 4 ß m tu 0 43 £- o c o z mt u OS V o o o o o o o o o o «H oo-a 0 neu u W O -H 44 V U in C 0 i-l O0T3 rt C 0 in o M in U 0 U 'H on e o M3 o o go 0 •H lH 44 0 P P- H £ U o IM e £#£ - v c a s T C rt m 0 0 1 rt O xrt 44 - lC -H as TTY Held Term rt c -H rt 43 05 •- IX 43 0 1- w e 0 3 cu U at 0 0 in - 0 «4 D XX E 0 C 0 42 44 •H O In O E •H 44 4 OCj H 01 in S m «4 m UT h it 0 44 a 4 0 e 0 en • H in £ M u 43 44 3 0 o «4 • H T3 l-i in 4 1 44 0 0 « C CO 11 13 43 rt • 0 0 O O 19 OS in 0 in C O en 144 u 0 O O -II 1i-H 4 rt -d • H 0T3 c 0 rt in OS VI _1 -H M « in 43 rt o 0 t43 o 0 •rt k «4 ••-I 00 144 0 44 ti IM •H ja in ■ in TJ E -rt m m U o 0 o 3 r w - 44 VI 0 3 • •a 0 T3 QJ —' in c 1- 0 O 44 in 4J C n 0 M 0 4-J frt 3 Silo 0 m o-x 110 nj 0 44 J D C cJi in -rt -I -H J-i o o •M -rt 44 44 •rt rt in u I r-t CM CO «t m 0 C- 0 o V Network Analysis Corporation the average rate of useful information being transmitted while columns 1 and m give the rates when overheads due to headers and partially tilled packets are included Columns g and h are conservative estimates of the bandwidth required by each device if it had a dedicated channel with sufficient capacity to handle the peak rate of the device Based on the assumptions made N people would generate 4175 bps into the terminals and 2645 bps out This makes no allowances for a packet header retransmissions artificial traffic due to repeaters acknowledgments or other overhead We assume a one frequency s stem with 100 Kbps channel capacity used in an unslotted Aloha random access mode See Section IV Using such a scheme conflicts due to interference between packets reduces the maximum bandwidth to l 2e of the nominal value or 18394 bps From Table 1 we see that N people will generate 15500 bps including overhead given a packet size of 1000 bits of information plus 250 bits of header Of the 15500 total bps only 6820 bps is useful information the rest is overhead--packet headers and wasted space from partly filled packets Thus the 1 channel has a possible maximum effective utilization of — - f ft 7 0 - TQ0 08093 yielding for the 100 Kbps channel a maximum rate of useful information of 8093 bps Recent studies indicate that a two data rate system with high rate repeater to repeater channels and low rate terminal to repeater channels may be desirable 9 7 Network Analysis Corporation It is instructive to compare the efficiency of an Aloha random access channel with schemes using dedicated channels for each device either by frequency or time multiplexing even though the implementation scheme for a conventional time division Oi frequency multiplexed scheme on the scale of the Packet Radio System is not clear The comparison given below is highly conservative since guard bands packet headers and synchronization requirements are ignored for the d ° 'icated channel systems Moreover if time division multiplexing were used system wide synchronization would be required If such synchronization were obtained the complexity of the hardware would be at least as great as that needed to implement a slotted Aloha scheme Such a slotted Aloha scheme would lead to a gain by a factor of two in channel utilization over the unslotted Aloha channel Finally It is assumed for ease of analysis that the packets in the Aloha system must all be of equal size the 1 e formula only applies to this case in the actual system packet size would vary - again increasing the utilization of the Aloha channel Tn columns g and h of I bie 1 w list the estimated dedicated channel capacity required for each device The total bandwidth required is then Etb g h 278720 bps The total average rate of useful rnloimation carried by t e channel is 6820 for ar effective utilization of 6820 278720 0244 Thus 9 8 Network Analysis Corporation a very conservative estimate is that the Aloha system is 3 to 4 times as efficient as dedicated channel systems and more realistically we can expect at least an order of magnitude improvement in efficiency when hardware complexity and actual overhead factors are considered The appropriate choice of N to scale the traffic is arbitrary Table 2 contains the number of stations the number of people per 100 Kbps channel the number of stations outside the large metropolitan areas and the population density at which the population associated with a station covers the same area as a repeater These numbers are all a function of N assuming a 100 Kbps channel In Table 3 the ratio of repeaters to stations is related directly to traffic density in bits per stcond per square mile For large N some stations would provide area coverage and thus replace repeaters The extent of the replacement depends on the distribution of population density The average population density in the U S is 57 6 people square mile the density in the states range from 0 5 people square mile in Alaska to 953 1 people square mile in New Jersey The density in Manhattan is 67 808 people square mile At high traffic levels N 10 000 or traffic density luO bps square mile repeaters play a much smaller rolt since the system is now traffic limited In extreme cases repeaters may not even be necessary The 148 Standard Metropolitan Statistical Areas SMSA with more tha 9 9 Network Analysis Corporation TABLE 2 N Stations People 100 Kbps Channel Repeaters Critical Station Outside Population SMSA's Density Stations Outside SMSA's 100 1712013 118 638312 02 38 1000 171202 1186 63831 16 3 78 10000 17121 11867 6383 1 65 37 77 100000 1713 118670 638 16 55 377 74 1000000 172 1186707 63 165 56 3777 41 TABLE 3 Traffic Densi ty bps sq mi 1 Sq miles per channel 100 Kbps or 8093 bps effects 'e No of Repeaters with 10 mile effect ive radius requir ed per station 25 8093 10 805 3 3 100 80 9 0 1000 8 1 0 10000 8 0 9 10 Network Analysis Corporation 200 000 population contain 127 417 000 of the 203 166 000 people in the United States in 301 661 square miles out of the 3 536 855 square miles of land area in the United States Thus the 148 SMSA's would correspond to enough area for 960 out of the 11258 repeaters many of which could be replaced by the stations for area coverage In the remaining part of the U S 10 JU8 repeaters would be required We can alread draw several preliminary conclusions from this simple analysis For low traffic levels N 100 000 or traffic density 1C bps sq mi the number of stations numbers of repeaters number of terminals hence the assignment of functions to devices should be such that the terminal is as simple and cheap as possible the repeater only slightly more sophisticated and as many functions as possible should be delegated to the relatively few stations and the point-topoint packet communication network connected to them We now turn to a more detailed examination of the Packet Radio Network 9 11 Net-vck Analysis Corporation 3 NETWORK NODES - TERMINALS REPEATERS STATIONS In this section we discus the devices1 functional cap- abilities which are necessary for communication in the Packet Radio network Terminals There are two categories of terminals i those which usually await a response to a message they transmit e g manually held radio terminals small computers and ii those which do not requne such responses or acknowledgements e g unattended sensors position indicators Some terminals in the former category will usually send and or receive several packets in one message Necessary or desirable capabilities of a terminal 1 Ability to identify v hether the packet is addressed to its ID 2 Calculation of packet checksum 3 Character generator logic 4 A random number generator for retransmission or an assigned random number for this purpose 5 Capabilities related to packet routing such as terminating retransmission when acknowledged recording and using a specific ID of a repeater and or station to be used for other packets of the same message counting the number of retransmissions 6 Capabilities related to the response to previously determined types of error see also Roberts 1972 a 9 12 Network Analysis Corporation 7 For unattended terminals capabilities by which a centralized control or a station will be able to identify whether the terminal is operative or dead Repeaters Functional capabilities for repeaters include 1 Calculating packet checksum 2 Packet storage and retransmission 3 Capabilities by which a station can determine whether a particular repeater or any repeater in a particular area is operative or dead 4 Capabilities 1 4 and 5 of terminals 5 Capabilities dependent on the routing strategy for calculating the most efficient next repeater on a transmission path to the station The routing functions in each of the three devices Stations Repeaters and Terminals will at least initially be implemented in software on a micro-computer The implementation of the routing algorithms will be described in a forthcoming report Stations The station will have a broadcast channel for communication with the Packet Radio network terrestrial channels for communication with the high speed point-to-point network and possibly a satellite channel Among the stations' functional capabilities are 1 Cryptographic apparatus suitable for handling sensitive and private messages 2 A directory of terminals and repeaters in its region 3 Operations necessary to convert packets from the 9 13 Network Analysis Corporation Packet Radio System into packets used in the point-to-point network and conversely 4 Storage buffers for packets received from terminals and for packets to be transmitted to terminals 5 Storage for character position information for active terminals 6 Character generation logic 7 Accounting capabilities 8 Capabilities related to routing of packets Adaptive Power One can resolve conflicting power requirements between urban and rural use of terminals by having transmission power adapt to the local requirements This is usually what people do when they speak and cannot be heard Specifically every device retransmits a packet with increased power until acknowledged up to some maximum specified number of times This increases its probability of being captured each time If the transmission is not successful because of collision with another packet an increase in the transmission power of both transmitters will not resolve the problem Many aspects of this approach need study General power considerations for the Packet Radio System are discussed in Propagation Considerations and Power Budget 9 14 Col 1974 Network Analysis Corporation 4 NETWORK LINKS - THE CHANNEL Communication between devices is by broadcast using a variant of the Aloha random access method Many aspects of the broadcast channel are of peripheral interest in the network design of the system however some factors are crucial to determine the behavior of the network By Aloha transmission we mean the use of a channel which is randomly accessed by more than one user In the simplest case users transmit equal size packets each using a speed equal to the channel speed operation are possible Several modes of The two simplest are a non-slotted asynchronous mode in which users can access the channel at any time and a slotted synchronous mode in which users can access the channel only at the beginning of a slot of time duration equal to a packet transmission time In the latter case a form of synchronization is required since each user must determine the beginning time of each slot The following theoretical results assume that if two or more packets overlap none is correctly received and each must be retransmitted Such a system is called a system witnout capture The simplest analytic results assume that there are an infinite number of users and that the point process of packet origination and the point process of packet originations plus retransmissions are Poisson with mean S and G respectively constant transmission time T for each packet is also assumed Then if a packet begins at some random time the probability 9 15 Network Analysis Corporation that it is correctly received no overlapping collision or con- 2GT flict in the nonsloted case is e The reception rate equal to the origination rate assuming that colliding packets are re- 2GT The effective transmitted until correctly received is S G e - 2GT channel utilization is ST GT e and the maximum utilization is Max S T l 2e For the slotted case the probability of - GT collision is e which leads to 1 e as the maximum utilization GT the channel traffic is equal to 1 2 and 1 at a maximum effective utilization for the non-slotted and slotted case respectively Abramson 1970 In the original Aloha system implemented at the University of Hawaii Abramson 1973 a central station communicates with several remote sites The system contains two channels - one fur station to site traffic and the second for site to station traffic This has several dVantages for the Aloha system First the station broadcasts continuously to furnish synchronization between all sites Second station to site traffic is coordinated by the station so that messages from the station do not collide with one another Thus if the traffic from the station has a separate channel from the reverse traffic retransmissions are substantially reduced Allocating separate channels for inbound and outbound station traffic is not as attractive when repeaters and multiple stations are introduced This channel allocation problem is examined in detail in a forthcoming report Channel improve ments also appear to be possible by using Spread Spectrum Coding 9 16 Network Analysis Corporation which offers the possibility of time capture Competing packets arriving during the transmission time of the first may be ignored if their signal strength is not too great When the trans- mitters are widely distributed geometric or power capture is also possible Roberts 1972 b With or without spread spec- trum a competing signal whicn is much weaker further away then the desired signal will not interfere Both types of cap- ture can give rise to performance superior to that predicted by the simple unslotted Aloha model However capture bia s against more distant transmitters since the probability of a successful transmission to the station decreases as the distance from the station increases Hence the number of retransmissions increases as well as the delay In Chapter 12 spread spectrum coding is evaluated as a function of 1 the packet arrival rate 2 the time bandwidth product K extent of spectrum spreading 3 the signal to noise ratio SN 4 the power law assumed for the transmission power of a transmitter at distance r from the receiver and of 5 the multiplicity of receivers available at the receiving location Channel properties and spread spectrum techniques are discussed in detail in three reports by Stanford Research Institute Measurement and Propagation SRI 1974a RF Capacity Considerations SRI 1974b and Spread Spectrum SRI 1974c 9 17 Network Analysis Corporation 5 NETWORK TOPOLOGY - REPEATER AND STATION LOCATION Many more factors affect the location of repeaters and stations than the simple ones discussed in Section II The cal- culations used to determine terminal to station fanouts and repeater to station fanouts neglect important considerations Moreover considering repeaters as area covers and stations as traffic covers reglects interactions between the two types of devices In this section we identify complicating factors as well as indicate methods for choosing locations for repeaters and stations Factors affecting the location of repeaters and stations in addition to range and traffic are i Logistics Some locations for repeaters may be preferable to others because of greater accessibility or more readily available power eliminating the need for batteries e g on telephone poles or near power lines Stations should preferably be placed near existing facilities of the associated point-topoint network ii Reliability and redundancy For many reasons redun- dant repeaters and stations will be required Since repeaters in remote areas will operate on batteries it will be necessary to have sufficient redundancy so they need nr t be replaced immediately Sta- tions and repeaters will have intermittent and catastrophic failures for which backup is required Extra repeaters are needed when line of sight to the primary repeater is locally blocked Random varia- tions in repeater and station manufacture and placement will cause 9 18 I Network Analysis Corporation I inadequate performance These factors will mandate a safety mar- gin of redundant coverage in the design When a single channel is operated in an unslotted Aloha landom access mode no more than l 2e of the bandwidth can be used as discussed in the previous section However additional traffic is generated by repeaters and conflicts created by transmissions between adjacent stations Some sources of re- transmissions are a For reliability several repeaters or statiois must be within range of each terminal If the repeaters retransmit every packet they receive one message can generate an exponentially growing number of relayed messages To prevent one message from saturating the network traffic control is required The disci- pline chosen and its efficiency will probably be the single most important system factor affecting system performance Two types of undesirable routing through the repeaters can occur First a message can circulate endlessly among the same group of repeaters if not controlled Second even if no message is pro- pagated endlessly a message an be propagated to a geometrically increasing number of new repeaters in a large network b For system reliability more than one station must be able to transmit via repeaters to each terminal Thus there can be conflicts between adjacent stations which reduces the useable bandwidth and also introduces coordination and routing problems 9 19 Network Analysis Corocrätlon c In general there will be many routes between any given terminal and any given station Consequently more con- flicts can result than would be the case if rhe terminals communicated directly with a station Extr»neouü traffic can also be generate- in the pointto-point network if several copies of the same message enter the network from different stations These duplicates can be identi- fied and eliminated either on entry to the stations or at the destination In the latter case traffic is artificially ir-creased and in the former case additional computation must be performed by the stations to maintain coordination In a forthcoming report several methods are de- scribed for locating repeaters to furnish reliable line of sight coverage of an area containing mobile or fixed terminals at unspecified locations Repeaters must be located so that any terminal will be in line of sight of a repeater and sufficient connectivity will be assured We wish to minimize the number of repeaters subject to this reliability of service constraint It is impractical to consider the infinite number of possible locations for repeaters and terminals Thus we 3imit consideration to finite sets of possible repeater and terminal locations The choice of these sets will be of great computa- tional importance and will probably be based on an adaptive selection process For the present we assume these sets are knov r and fixed 9 20 Network Analysis Corporation Next the possibility cf line-of-sight transmission between pairs of points must be determined In general these procedures depend on many factors including effective earth radius fresnel zones weather conditions design height and orientation of the antenna and topography between the two points are beyond the scope of the discussion here These factors Nevertheless we assume there are known functions which indicate if a repeater at a location can communicate with a terminal or a repeater at another location More generally we can consider the probability that the appropriate two locations can communicate Amonf he initial problems is the proper choice of a reliability measure We assume that the packet radio network is for local distribution collection of data from terminals with small traffic rales compared y c the channels' capacity so that throughput is not a major reliability consideration That is if any path through the networl exists for a given pair of terminals we assume there is sufficient capacity for transmission Possible measures of r stwor1 reliability that have proven useful in the analysis of communication networks Van Slyke and Frank 1972 are the probability that all terminal pairs can communicate and the average f Ltior of terminal pairs which can communicate For the network design problem as dirtinguished from the analysis problem known probabilistic approaches appear inefficient from ooth computcicional and da a collection points of view This suggests that deterministic requirements such as thers exist K node disjoint iths between every terminal pair should be considered in the design stage 21 This guarantees that at least Nef ork Analysis Corporation K repeaters or transmission links must fail before any terminal pair is disconnected In a report in preparation this problem is an amalgam of two well studied network problems the set covering problem Garfinkel and Nemhauser 1972 Roth 1969 and the minimum cost redundant network problem Steiglitz Weiner and Kleitman 1969 9 22 Network Analysis Corporation CHAPTER 10 ROUTING AND ACKNOWLEDGEMENT SCHEME FOR THE PACKET RADIO SYSTEM 1 INTRODUCTION In this chapter we discuss routing problems for broadcast oriented packet communication networks Possible solutions to these problems are described and an approach tested by simulation is proposed for system operation There are basic differences between the packet radio network and existing point-to-point store and forward networks such as the ARPANET For example the packet radio network serves mobile terminals devices in the network share a common channel in a random access broadcast mode and repeaters in this network will have significantly less storage and processing capabilities than the switching nodes in ARPANET like systems Consequently many of the routing techniques developed for the point-to-point networks are not directly applicable to the packet radio network The objective of the network is to distribute and collect traffic to and from terminals which have high ratios of peak to average traffic requirements An initial test of the packet radio system is to serve as a local distribution system for traffic dastined for the ARPANET from mobile sources The network consists of repeaters to provide area coverage and stations to provide traffic management and interfaces to other nets Stations serve as a major source and sink for the packet radio net There are many possible paths via repeaters over which a packet originating at a terminal may flow to reach a station That is a packet transmitted from a terminal can be received by several repeaters and there may be several stages of transmission through repeaters before the packet is received by a station Some problei s ha arise in controlling traffic flow in a large scale broadcast network are 10 1 Network Analysis Corporation 1 A packet transmitted can be received by many repeaters or stations or not be received by any 2 Many copies of the same packet can circulate in the broadcast network 3 Many copies of the same packet can enter the point-to-point network at different stations Indications of the consequences of not imposing a suitable flow control mechanism can be observed from combinatorial models analyzed in Chapter 11 In these ideal models the repeaters are located at corner points of an infinite square grid and time is broken into unit intervals each slotted into segments A packet transmitted by a repeater can be received only by its four nearest neighbors If a packet is correctly received by a repeater it is retransmitted within the next unit interval of time at a random time slot within the interval Suppose now that a single packet originates at the origin and that the transmission plus the propagation time falls within one unit interval of timv» Then after n intervals of time i the number of repeaters which receive the packet for the first time B n is B n 4n n i B 0 1 ii the number or repeaters through which the packev passed A n is n A n I B j 2n j-0 2 2n 1 n o 10 2 Network Analysis Corporation iii if we assume that a repeater can receive antrelay a large number of packets within the same time interval the number of copies of the same packet received by a repeater at coordinates d j after d 2k units of time is o N° d 2k d 2k k j J ak yy Air f r large k 2 where d is the number of units of time that the packet requires to arrive from the origin to the repeater and j is the horizontal number of units Unless adequate steps are taken the explosive proliferation of redundant packets will severely limit the capacity of the system One can now recognize two somewhat distinct routing and control problems 1 to ensure that a packet originating from a terminal arrives at a station preferably using the most efficient shortest path and 2 to suppress copies of the same packet from being indefinitely repeated in the network either by being propagated in endless cycles of repeaters or by being propagated for a very long distance In Section 2 we outline general techniques wh ch can be combined to provide workable routing schemes Acknowledgement schemes aimed at achieving high throughput and minimum delay are discussed in Section 3 Section 4 gives a detailed description of an efficient routing scheme In Section 5 a method for repeater labeling to obtain efficient routing is proposed Finally some quaiitatixre properties of the routing scheme proposed in Section • generated via a detailed simulation are given in Section 6 1C Network Analysis Corporation 2 POSSIBLE ROUTING TECHNIQUES There are two key objectives in developing a routing procedure for the packet radio system First we must assure with high probability that a message launched into the net from an arbitrary point will reach its destination Second we must guarantee that a large number of messages will be able to be transmitted through the network with a relatively small time delay The first goal may be thought of as a connectivity or reliability issue while the second is an efficiency consideration A rudimentary but workable routing technique to achieve connectivity at low traffic levels can be simply constructed by using a maximum handover number Boehm Baron 1964 and saving unique identifiers of packets at each repeater for specified periods of time The handover number is used to guarantee that any packet cannot be indefinitely propagated in the net Each time a packet is transmitted in the net a handover number in the header is incremented by one When the handover number reaches an assigned maximum the packet is no longer repeated and that copy of the packet is dropped from the net Thus the packet is aged each time it is repeated until it reaches its destination or is dropped because of excessive age If the maximum handover number is set large extensive artificial traffic may be generated in areas where there is a high density of repeaters On the other hand if it is set small packets from remote areas may never arrive at stations This problem can be resolved as follows We assume that every repeate1 can calculate its approximate distance in numbers of hops to stations by observing response packets A labeling technique for this calculation is discussed in Section 5 The first repeater which received the packet from a terminal sets the maximum handover number based on its calculated distance from the station The number is then decremented by one each time it is relayed through any other repeater The packet is dropped when the number reduces to zero 10 4 Network Analysis Corporation When a station transmits a packet it will set the maximum handover number by knowing the approximate radius in repeaters in its region Even if a packet is dropped after a large number of transmissions local controls are needed to prevent packets from being successively bounced between two or a small number of repeaters which repeat everything they correctly receive Such a phenomena is called cycling or looping A simple mechanism to prevent this occurrence is for repeaters to store for a fixed period of time entire packets headers or even a field within the header that uniquely identifies a packet A repeater would then compare the identifier of any received packet against the identifiers in storage at the repeater If a match occurred the associated packet would not be repeated The time allotted for storage of any packet identifier would depend on the amount of available storage at a repeater and the number of bits required to uniquely identify the packet For example more than 4K packets could be uniquely identified with 12 bit words Thus 4K of storage could contain entifiers for more than 300 packets With a 500 Kbps repeater to repeater common channel for broadcast and receive and 1 000 bit packets this would be sufficient storage for over 1 5 seconds of transmission if the channel were used at full rate Assuming a single hop would require about 20 milliseconds of transmission and retransmission time a maximum hop number of 20 would guarantee that any packet would be dropped from the system because of an excessive number of retransmissions long before it could return to a previously used repeater not containing the packet identifier The combination of loop prevention and packet ageing with otherwise indiscriminate repetition of packets by repeaters will guarantee that a packet travels on every available path a maximum distance away from its origin equal to its original handover number 10 5 ■HMHHRU Network Analysis Corporation Thus if the maximum handover number is larger than the minimum number of hops between the terminal and the nearest station a packet accepted into the net should reach its destination Unfortunately with this scheme copies of the packet will also reach many other points with each repetition occupying valuable channel capacity However if those packets for which adequate capacity is not available are prevented from entering the net the network will appear highly reliable to accepted packets The above routing scheme is an undirected completely distributed procedure Each repeater is in total control of packets sent to it and the stations play no active part in the systeiu s routing decisions They must still play a role in flow control In the above procedure no advantage is taken of the fact that most traffic is destined for a station either as a terminus or as an intermediate point for communication with the ARPANET Also the superior speed and memory space of the station is ignored For efficiency one is therefore lt-ü to investigate directed hierarchical routing procedures A directed routing procedure utilizes the stations to periodically structure the network for efficient flow paths Stations periodically transmit routing packets called labels to repeaters to form functionally a hierarchical point-to-point network Each label includes the following information i a specific address of the repeater for routing purposes ii the minimum number of hops to the nearest station and iii the specific addresses of all repeaters on a shortest path to the station In particular the label contains the address of the repeater to which a packet should preferably be transmitted when destined to the station When relaying a packet to its destination the repeater addresses the packet to the next repeater along the preferred path Only this addressed repeater will repeat the packet and only when this mechanism fails will other repeaters relay the message A detailed description of the directed routing technique proposed is 10 6 Network Analysis Corporation given in Section 4 However we first discuss acknowledgement structures for message flow since good acknowledgement schemes are an integral part of an efficient routing procedure I 10 7 Network Analysis Corporation 3 ACKNOWLEDGEMENT CONSIDERATIONS Acknowledgement procedures are necessary both as a guarantee that packets are not lost within the net and as a flow control mechanism to prevent retransmissions of packets from entering the net Two types of acknowledgements are common in packet oriented systems 1 Hop-by-Hop Acknowledgements HBH Acks are transmitted whenever a packet is received successfully by the next node on the transmission path 2 End-to-End Acknowledgements ETE Acks are transmitted whenever a packet correctly reaches its final destination within the network In a point-to-point oriented network such as the ARPANET HBH Acks are used to transfer cSponsibility and thus open buffer space for the packet from the transmitting node to the receiving node This Ack insures prompt retransmission should parity errors or relay IMP buffer congestion occur The ETE Ack serves as a flow regulator between source and destination and as a signal to the sending node that the final destination node has correctly received the message Thus the message may be dropped from storage at its origin Both types of Ack's serve to ensure message integrity and reliability If there is a high probability of error free transmission per hop and the nodes have sufficient storage the Hop-by-Hop scheme is not needed for the above purpose Without an HBH Ack scheme one would retransmit the packet from its origin after a time out period expired cie introduced the HBH Ack to decrease the delay caused by retransmiss ons at the expense of added overhead for acknowledgements In the ARPANET this added overhead is kept small by piggybacking acknowledgements whenever possible on information packets flowing in the reverse direction In the packet radio system the overhead can be kept small by listening whenever possible for the next 10 8 Network Analysis Corporation repetition of the packet on the common channel instead of generating a separate acknowledgement packet The value or an End-to-End acknowledgement is sufficiently great that it can be assumed present a priori However the additional use of a Hop-by-Hop acknowledgement is not as clear Therefore in this section we examine the question of whether the ETE Ack is sufficient or whether one needs a Hop-by-Hop HBH acknowledgement in addition The problem is therefore whether an HBH Ack is superior to an ETE Ack with respect to throughput and delay since the ETE Ack ensures message integrity It is noted that the routing and flow control by devices in the network depend on the type of acknowledgement scheme used We consider a simple case where n-1 repeaters separate the packet radio terminal from the destination station Assuming that the terminal is at a distance of one hop from the first repeater one obtains the following n-hop system fr hop Jq R hop 2 f i - • i Xs h °P n ® A simple model is used to evaluate the total average delay that a packet encounters in the n-hop system when using HBH and ETE acknowledgement schemes When the ETE acknowledgement scheme is used every repeater transmits the packet a single time If the packet does not reach the station retransmission is originated by the terminal The ETE acknowledgement is sent from the station In the HBH scheme repeaters store and retransmit the packet until positively acknowledged from the next repeater stage If after a terminal or a repeater in the HBH case transmits the packet an acknowledgement does not arrive within a specified periou of time it retransmits the packet The waiting period is composed of the time for the acknowledgement to arrive when no conflicts occur plus a random time for avoiding repeated conflicts 10 9 Network Analysis Corporation Two different schemes for LTE acknowledgement and one scheme for HBH acknowledgement are studied Curves for the total average delay as a function of the number of hops and the probability of successful transmission per hop are obtained Two cases are considered One in which the probability of success is constant along the path ana another in which the probability of success decreases linearly as the packet approaches the station Finally channel utilizations are compared when using ALOHA Abramson 1970 1973 random access modes of operation It is demonstrated that the HBH scheme is superior in terms cf uelay or channel utilization This conclusion becomes significant when the number of hops increases or when the probability of successful transmission is low for example in a five ho system if the probability of success per hop is 0 7 then the total average delay is 12 5 and 53 jacket transmission times for tne HBH and ETE acknowledgement schemes respectively The model used is based on Kleinrock Lam 1973 Roberts The model is simplifiea however by assuming that the probability that a packet is blocked is the same when the packet is new or has been blocked any number of times before Although the more general equations could have been written the numerical solution is rather elaborate Kleinrock Lam 1973 and seems unnecessary for this comparative study It is further assumed that the probabilities of being blocked on different hops are mutually independent The total delay is defined as tne time between the transmission of the first bit by the terminal and the correct reception of the last bit of the packet by the station 3 2 DELAY CONSIDERATIONS The delay equations normalized by the number of packet transmission times are given by D HBH 1 n l 2r • o 1 1 10 10 i-q c i 1 Network Analysis Corporation D ETE 1 6 • n l 2ß a «n ö 2 D2 ETE 1 ß • n l 2ß a 6 3 In these equations a is the ratio of the acknowledgement transmission time to the packet transmission time 8 is the ratio of the average propagation time per hop to the packet transmission time and 6 is the ratio of the average waiting time beyond the minimum for avoiding repeated conflicts to the packet transmission time The quantity q is the probability of successful n transmission on hop i and Q TT q i l 1 As indicated before two different cases for the ETE acknowledgement are considered D ETE represents the delay when the terminal waits the expected time for the packet to reach the station and for the ETE acknowledgement to be received by the terminal before retransmitting the packet D- ETE is for the case in which the terminal retransmits after shorter periods of time because it anticipates a lov probability of successful transmission Q In particular we examine the case in which the retransmission delay is -he same as in the HBH method Figures 1 2 and 3 show delay curves for the three acknowledgement schemes u ing the parameters a 0 5 ß 0 02 and 6 2 0 Figures 1 and 2 are for the case in which q is constant along the path The curves show the delay as a function of the probability of successful transmission q rather than the channel utilization Thus they can be used for slotted or non-slotted ALOHA or possibly for other access schemes It is evident from Figure 1 that the delays for the ETE acknowledgement schemes grow much more rapidly than delays for the HBH scheme For example in the 5-hop system if the packet transmission 10 11 lOOOr 01 0 e -H c o -H OJ CO •H e W c ra 100- H EH 4J 0 U ro 04 C •H i 0 i-4 d Q $ 10«- n 2 n 5 n 10 FIGURE 1 Probability of Success - q 1 0 0 8 0 6 - 0„4 10 12 0 2 lOOCL- T -f- in a E c o ■H » c M c 3 J O 100-- M 0 m ru c I 4 ■H o Q 10 g 0 8 g 0 5 g 0 4 FIGURE 2 Number of Hops - 6 10 ft 10 'fTiiimaariiiiiiiBiiiiiiiiiTiiiiiii'iiii 1000 - 0 I c o ■H to 0 •H ß D ETE CO c n 100 0 A ü 0 ß i id H D a 10 q 0 9 - 0 5 -r i n Number of Hops - n FIGURE 3 ■ ■ 6 7 10 14 10 Network Analysis Corporation time is 10 msec the average delays are 170 msec 470 msec and 1180 msec for D HBH D ETE and D fETE respectively In practice q will differ along the path It is reasonable to assume that the probability of success q will decrease when the packet approaches the station this assumption Simulation results confirm When random access ALOHA systems are used the practical range for q is from 1 e for which the effective utilization is maximum to 0 9 for which the utilization is 4 7% and 9 4% for the non-slott-cd and slotted case respectively We take a function of the form qt 0 9 - 0 5 -i- i « 1 2 n 4 The normalized average delay as a function of n with q as in Equation 4 is shown in Figure 3 3 3 EFFECT ON CHANNEL UTILIZATION We now consider the effect of the acknowledgement scheme on the maximum utilization achievable when using slotted and nonslotted ALOHA random access schemes To simplify the comparison we take 6 0 this affects the comparison with ETE scheme 1 and assume that q is constant along the path It is further assumed that the arrival process to each repeater of new packets and new packets plus retransmissions are both Poisson with mean rates S and G respectively and that the packet transmission time is one unit Given an n-hop system suppose that one wants to use an ETE acknowledgement scheme such that the average delay equals that when using a HBH scheme Equating 1 and 2 and 1 and 3 respectively one obtains We use subscripts 1 and 2 to denote variables for ETE schemes 1 and 2 respectively variables without a subscript will denote quantities related to the HBH scheme 10 15 Network Analysis Corporation «1 ' « '• '2 - ir-- I7q 5» The relation between the channel traffics G for the acknowledgement schemes when using slotted ALOHA are G In -£- G 2 V n 6 n -6 n- n-l e 7 where Consequently the channel utilizations or throughputs S are related as follows i 4 -« 1-4- s n m fl £l Yyl n 9 S nG £ ny -1 The rr tios of utilization Equations 8 and 9 as a function of n are shown in Figure 4 for the case G 0 5 which is equivalent to 30% utilization in the slotted ALOHA random access system 10 16 - O o °o o Q W EH EH O to Pn O ■ • vu ff 3 tU O g X w §D - »in 2 • » ■ n N 10 17 3 O H Network Analysis Corporation 4 A DIRECTED ROUTING PROCEDURE In this section a routing scheme is proposed aimed at achieving maximum throughput and minimum delay This is obtained by using shortest path minimum hop routing from terminal to station and from station to terminal and by preventing whereever possible duplicate copies of a packet from being circulated in the network However the routing procedure includes sufficient flexibility so that when the first choice shortest path cannot be used the packet departs from this path and uses a shortest path from its new location One pays overhead for this efficiency by carrying two labels in the packet header 4 1 LABELING The shortest path routing is obtained by labeling the repeaters to form functionally a hierarchical structure as shown in Figure 5 Each label includes the following information i a specific address of the repeater for routing purposes ii the minimum number of hops to the nearest station and iii the specific address of all repeaters on a shortest path to the station and the address of the repeater to which a packet has to be transmitted when destined to the station For simplicity we describe routing for the case of a one station network A label of repeater R of hierarchy level j will be denoted by L i j l _ ■ ■ __ The station will have the label L i ■ 11 L° will denote the label of the repeater which is the nearest available to the communicating terminal A label is composed of H subfields where H is the maximum number of hierarchy levels H-l is the maximum number of hops on the shortest path between any repeater ard the station Every subfield has three possible entries blar k BLK a serial number SER or ALL L has j entries SER's and H-j BLK's as shown below 1 2 i-i i i i H SER SER SER SER BLK BLK v - j serial numbers - H-j blanks 10 18 10 19 Level 1 Level 2 Level 3 a TE R37wa 'm - FIGURE 5 Network Ana fysis Corporation Network Analysis Corporation We say that LJL- homes on I»k hfL Lk if p j-1 and the first j-1 subfields of both are identical If two repeaters at level j home on the same repeater their labels will differ only in the entry to subfield j As an example if we use 3 bits per subfield the labels of the station and the repeaters of the network shown in Figure 5 are as follows ll Subfield 1 0 0 1 Subfield 2 0 0 0 Subfield 3 0 0 0 J 12 0 0 1 0 0 1 0 0 0 J 22 0 0 1 0 1 0 0 0 0 J 33 0 0 1 0 0 1 0 0 1 J 43 0 0 1 0 0 1 0 1 0 '53 0 0 1 0 1 0 0 0 1 '63 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 J J 73 In this example a subfield in which all bits are 0 is considered blank Note that all entries in Subfield 1 are the same since all repeaters home eventually on the same station 4 2 ROUTING The packet header in both directions will include the following routing information L kn TO L °U OTHER HEADERS AND PACKET INFORMATION LABEL OF NEAREST REPEATER TO THE TERMINAL i 2Ü Network Analysis Corporation L is the label of the repeater to which the packet is currently addressed The complete packet will always be transmitted to a specific device other devices which may receive the packet will drop it The shortest path from a terminal to the station consists of L0 h L° h h L° # up to L in the given order and in the reverse order when routing from station to terminal When a specific repeater along the shortest path is not known by the terminal or not available then the terminal or repeater which has the packet will transmit only ehe header part of the packet trying to identify a specific repeater In that case the label L will include some entries ALL A Routing from Terminal to Station When a previously silent terminal begins to communicate it first identifies a repeater or a station in its area It transmits only the header part of the packet with all entries in L set to ALL The header is addressed to all repeaters and stations that can hear the terminal A device which cor»-' Ctly receives this header substitutes its label n the space L and repeats the header This particular L is also L° and will be used by the terminal to transmit all packetr during this period of communication If a terminal i •• stationary it can store this label for future transmissions L° xn begins to transmit the complete packet along ehe shortest path to the station Suppose that L along the shortest path is not successful in transmitting the packet to h L Then L begins the search stage of trying to identify another repeater in the first step it tries to identify a repeater which is in level p j-l This is done by using the following label 1 2 3 j-1 j j 1 SER ALL ALL • 10 21 • • ALL BLK BLK • •■ ■ BLK Network Analysis Corporation The header is addressed to all repeaters in levels 2 to j-1 which eventually home on L If this step is not successful in the second last step L • tries to identify any available repeater by using a label in which the first entry is SER and all other entries are ALL When a specific repeater is identified and receives the packet it transmits the packet on the shortest path from its location Note that if repeaters have sufficient storage they can save alternative labels and thus reduce the necessity of searching for a specific repeater Alternative solutions in which repeaters have multiple labels are also possible B Routing from Station to Terminal L° contains sufficient information for shortest 13 path routing to the terminal Denote by h -1 the inverse -2 -l -l of h and by h h h etc The shortest path from station to terminal includes h ' 1 L° h I 2 L o h L° and L° If some L is not successful lj ij kp in transmitting the packet along the shortest path it begins the process of identifying another specific repeater Note that when routing to the station the next label is always a function of the label of the repeater that currently stores the packet When routing to the terminal the next label is a function of L° and the hierarchy level of the repeater that currently stores the packet Thus when routing to the terminals it will be useless to transmit the packet backwards since it will usually arrive back at the current location therefore it is more efficient to delay the packet If when routing to the terminal a repeater on the shortest path is temporarily unreachable the procedure attempts to by-pass Network Analysis Corporation this particular repeater and regain the original shortest path route 3 by h L° 13 The labels that will be used are shown below j-i h'Vij 1 2 SER I SER rsEir h-2 SER SER j-3 I SER j-2 j-1 j I SER I BLK BLK I SEARCH SER SER j-3 TSER- SER I ALL I BLK J-3 j-2 BLTT j-2 BIX ■BUT j-1 j i BUT rBnr j-H BLK BLK I j l BTT BLK All the entries SER are taken from L° 1 4 3 ACKNOWLEDGEMENTS In Section 3 it has been shown that the use of HBH ack- nowledgements in the routing scheme in addition to the ETE acknowledgement is desirable However one can prevent specific acknow- ledgement packets from being transmitted by using the passive echo acknowledgement This approach has other advantages as well which will be described in the next section be employed along the path Echo acknowledgement will That is the device transmitting the packet waits in a receive mode to receive this same packet when it is repeated by the next stage The reception of the packet when transmitted by the next stage constitutes the acknowledgement since it indicates that the next repeater stage has correctly received the packet and will store and retransmit it as necessary In fact one has the option of adding parity bits after the header In this event it would be sufficient to hear the header of the packet and thus the header plus parity bits will constitute the acknowledgement At the end of a path the terminal or station will repeat the header Note that the probability of correctly receiving an acknowledgement would be higher than the probability of correctly receiving a packet due to the difference in transmission 10 23 vuKomMMBiMiilKhkSS Network Analysis Corporation time Furthermore in many cases the station may correctly receive the header whereas the entire packet is received in error The information contained in the header can be used by the station for control purposes 4 4 TRAFFIC CONTROL The control procedures to be implemented would use control packets from stations to repeaters from stations to terminals and possibly from repeaters to terminals Some of these may be implemented in the station - repeater protocol and relate to the initialization of repeaters relabeling of repeaters under various overload conditions activation and deactivation of repeaters and so on In this section we discuss controls necessary for the routing scheme These are i Initial search by the terminal ii Maximum handover number MHN iii Maximum number of transmissions MNT It was demonstrated in Kleinrock Lam 1974 that after channel traffic exceeds a certain value throughput reduces If the number of retransmissions is not limited the offered channel traffic will increase indefinitely and the throughput will reduce to zero Thus one problem is to prevent new traffic from entering the system when the system is congested This control can be obtained by the search procedure which is used by terminals when entering the system This control is local in the sense -hat it depends on the traffic level in the geographical neighborhood of the terminal Terminals will nevertheless be able to enter the system when being far from stations and the traffic introduced will propagate towards the stations The MHN is a control aimed at suppressing packets from being propagated in endless cycles of repeaters or being propagated over path-- containing many hops This may occur when packets depart 10 24 Hn my Network Analysis Corporation from the shortest path Furthermore if the routing scheme used is relatively unsophisticated the MHN will prevent the packet from arriving at remotely located stations The MHN for a given packet depends on the number of hops between the originating terminal and the station with which it communicates or vice versa It will therefore be a function of the hierarchy level of the repeater with the label L° The MNT is also a local control which reduces the traffic level when the system is congested by discarding a packet after a specified number of retransmissions have been attempted It also prevents repeaters from indefinite transmission of a packet when surrounding repeaters are temporarily blocked and are unable to accept packets 4 5 PACKET FORMAT A possible packet format for performing the routing described is shown below HEADER PACKET INFORMATiON PARITY The header includes the following items T F C I DID OID J kn i MHN E C T F - a bit indicating whether the packet is addressed To station or From station C I - a bit indicating whether the packet is a Control packet or an Information packet DID - Destination address OID - Origination address L The label of the repeater to which the packet is currently addressed kn L° ID The label of the repeater nearest tc the terminal which originated the packet or to which the packet is transmitted MHN Maximum handover number - 10 25 -■ '•' ■■■■ -'f L-'-¥- i n iJBBnfflfa aSii g jY N'twork Analysis Corporation E C - An error or control message If it is an information packet the space may include a sequential number specification of the packet nuruber in the message etc If it is a header packet it may include an error message asking for retransmission of a certain number of packets If it is a control packet from the station this space may be used for the control message 10 26 Netwi rk Analysis Corporation 5 A PROCEDURE FOR REPEATER LABELING In this section we identify some of the problems of repeater labeling and propose one approach for the initial labeling of a repeater network Assume that initially every station and repeater has a fixed ID R This ID will be used for labeling purposes to identify whether the device is operative or dead to activate and deactivate a repeater and for other control purposes The station will determine and assign labels to all repeaters in its area in the initial labeling procedure When more than one station operates in an area the initial labeling will b done by the stations sequentially and repeaters may be allowed to choose the home station according to the minimum number of hops First it is necessary to specify two parameters i the maximum number of subfields or hierarchy levels say H and ii the number of bits per subfield say B These parameters are to be the same for the entire broadcast network in order to have the same packet format when transmitting information If some sections of the broadcast network are disjoint it is sufficient that B x H be the same for the entire network As indicated before H-i is the maximum number of hops that a packet will travel when using the shortest path route and 2 -2 is the maximum number of repeaters that can home on a single repeater or station one label is needed for ALL and another for BLK 2 x H x B is the number of bits in the header which will contain the routing information The initial labeling procedure is STEP I The station transmits a control packet to every repeater sequentially This packet includes an MHN as well as another MHN to be used by the addressed repeater for its response packet There is no directed routing at this stags every repeater which correctly receives the control packet decrements its MHN and stores and retransmits it until echo acknowledged by the next stage The control packet is dropped when its MHN reduces to zero 10 27 Maubu» Network Analysis Corporation The repeater to which this packet is addressed transmits a response packet to the station using the ass'gned MHN Every repeater which receives this packet will decrement the MHN ar«i add its R in order The station may receive one response packet several or none If no response packet is received the station can try several more transmissions each time increasing the MHN's or conclude that the repeater is dead this repeater can poss L be reached from another station STEP II The information acquired from the response packets is sufficient to determine a hierarchical labeling structure In this step the station processes the information and determines an optimized structure The processing performed during this step is described in the next section STEP III In this step the station tests the shortest path particularly in the direction from station to repeaters which was not tested before The station transmits a control packet to every repeater using its label The station uses an MHN equal to the number of hops on the shortest path so that if this path is not possible the repeater will not be able to receive the packet A repeater which receives this packet transmits a response to the station which constitutes an ETE positive acknowledgement If all repeaters have been successfully tested the procedure ends otherwise the program returns to Step II for further processing 5 1 AN ALGORITHM FOR DETERMINING THE LABELS We describe a technique for processing the response packets and for determining the hierarchical labels in Step II of the labeling procedure In general the repeaters may be distributed 10 28 Network Analysis Corporation at random locations and the station may not know the geographical locations of repeaters Furthermore there may be more repeaters than the number needed for efricient routing Ideally one would want to obtain a network of repeaters which has the following properties 1 There should be a minimum number of hierarchy levels 2 There should be a shortest path from every repeater to the station 3 The entire area should be covered with a minimum number of repeaters 4 Every repeater should be able to transmit directly to at least j say 2 other repeaters 5 The number of repeaters which home on one single repeater or station should be 2 -2 A solution which satisfies all the requirements may not exist B For example if more than 2-2 repeaters can directly reach the station and none can be deactivated requirement 2 will not be satisfied Suppose that there are N-l repeaters and one station denoted by R The station first constructs a connectivity matrix C c where 1 if device j can hear i directly i»j 1» 2 0 N otherwise C is constructed from the response packets in Step I For example then if a response from R x contains in order R 6 Rin R i c le l c em 1 c mk •- 1 One can see that the station does 10 29 «■wwMmta Network Analysis Corporation not have to transmit the first labeling packet to all repeaters since it can learn about the functional location of some of the repeaters which were on the return path of previous control packets Furthermore the number of response packets to a control packet can be increased when the MHN assigned by the station is increased Finally we note that C is not necessarily symmetric The entries 1 in row i indicate the repeaters to which R can directly transmit and the entries 1 in column i indicate the repeaters from which R can directly receive The structure of the repeater network will be recorded by the vector h where h j 1 N indicates the repeater on which R homes Let S m denote the set of repeaters whose shortest path to the station includes exactly m hops Assume that all repeaters in S l S 2 and S m have been labeled assigned home repeaters We describe the labeling of repeaters in S m 1 by repeaters of S m At every state k of labeling S m 1 by S m we characterize repeaters of S m by d k The number in S m 1 which have been labeled R say the degree of R at state k v k The number in S m 1 which still can be labeled R f k The potential degree of R at state k i e f k d k v k Repeaters of S m 1 will be characterized by u - The number of repeaters in S m which can label it At every state k we distinguish among three disjoint subsets of S m and S m 1 10 30 Network Analysis Corporation SF k R v k 0 cannot label more T R S k R 1 f k 2 -2 ordered according to increasing values ' of d k and when the same then according to increasing values of v k l R I B S k R f k 2 -2 ordered according to incr sing '■ T i„ f v k values of m x x a Ci k» -k öö n h k 0 already labeled assume that 1 ' h± 0 Ü c lp 1 for some Rp e S m k ordered according to m l k R l decreasing values of the number of repeaters in S m k that can label them and when this is the same then according to decreasing values of u l S S k The remaining repeaters of S m 1 ordered according to decreasing values of u Note that S m k is the set which can potentially violate requirement 5 and S L 1 k is the set to be labeled which may result in this violation Therefore one should try to label S m i k by S m k When such a label is assigned it decreases the p values of f k in S k Furthermore the orders of the subsets of S m according to d k are aimed at obtaining a network in which the repeaters of S m 1 are divided equally among repeaters of S m this was not specified in the requirements the order of S k is done so that if possible the repeater which can be labeled by the largest number of repeaters of 3 k is labeled first The algorithm proceeds as follows There may be repeaters in S m for which v 0 0 It is convenient to refer to these as end repeaters of level m since no repeater will home on these 10 31 Network Analysis Corporation SI P A Take the first of sj k and label it by one of SL k m i ■ m beginning with the first If it is labeled evaluate the subsets of state k 1 and do the same if not take the next repeater of S i k and do the same STEP B i If S k is empty then S_ k is also empty comR L plete the labeling cf SR 1i k k b 1 Y sm - using the procedure of Step A then return eturn to Step A H L ii If SR k k is not empt empty label one of Sm 1 k by m S k using the procedure of Step A then return to Step A R L Note that ii all of S m k becomes part of S m k at some state the network produced satisfies requirements 1 2 and 5 since 5 is satisfied by the last statement 2 implies 1 and 2 is satisfied by the definition of S m If one of the above requirements must be violated modification of ii in Step B of the algorithm is required The sets S m defined at the beginning of this section are constructed recursively as follows S 1 Rk c S m 1 R kl X Rk AJ S p Cj 1 for some R eS m i That is to construct S m 1 it is necessary to examine in the matrix C only the entries 1 in the columns which corresponds to repeaters of S m and choose the ones that have not been identified yet 5 2 REMARKS 1 The shortest path label assignment does not in general correspond to physical distance That is the label assignment depends on the terrain as well 10 32 Network Analysis Corporation as possible variations in transmission power and reception sensitivity of devices Thus it is a functional rather than a geophysical assignment 2 In the practical case it may be necessary to label redundant repeaters and then deactivate them for use as stand-by repeaters Furthermore the procedure for this process should satisfy requirements 3 and 4 of the previous section 10 33 _ 'J- - 6 SOME SIMULATION RESULTS A computer program v ich simulates in detail the operation of the packet radio network and the proposed routing and control techniques is currently available and will be described in NA 1974 b Some qualitative observations of the model's performance as related to routing are described in this section Figure 6 shows one network that has been extensively studied The labels of repeaters in this network were assigned a priori and the lines connecting the devices in Figure 7 signify the hierarchical structure created by the implementation of the directed routing technique Terminal traffic is introduced into the system at random times and originates at random locations on the plane Once a terminal is introduced it begins the search procedure and the communication between a terminal and a station proceeds using the routing and control schemes described including the ETE and Echo HBH acknowledgements Figure 6 shows the connectivity of the network simulated That is when a particular repeater transmits all devices connected to it by line can receive the packet Simulation results demonstrate that the critical hop in the packet radio network is between the first level repeaters and the station Thus special attention should be given to the flow control design on this hop In particular repeater placement in the neighborhood of the station and the control of these repeaters by the station are significant These repeaters also have higher power duty cycles since they repeat all packets o2 repeaters which home on them It is also demonstrated that there is a higher probability of end-to-end successful transmission from station to terminal than from terminal to station This is observed from the higher frequency of repeater searches and dropped packets when routing towards the station One cause is that the station is the largest user and thus has higher probability of successful transmission over 10 34 Network Analysis Corporation the critical hop because it manages its own traffic rather than competing with itself in a broadcast node The terminal simulated recognizes a packet addressed to it by checking a portion of the packet header not related to repeater labels Consequently the terminal can receive from a different repeater than the one to which it transmits Since the response to a search packet by repeaters is randomized in time the terminal frequently identifies a repeater which is not necessarily the nearest to the terminal or the nearest to the station As a result the path from the terminal to the station is not necessarily the same as rom the station to the terminal The latter is usually shorter Such a case is illustrated in Figure 8 Here the terminal will usually receive its packets from Rl at the time Rl transmits to R2 The echo by the terminal will usually acknowledge Rl and R2 simultaneously Furthermore R3 need not handle traffic to the terminal Figures 6 and 7 show that while the station has connectivity 7 only 4 of these repeaters are labeled as first level repeaters that home on the station In particular note that the station can hear all packets transmitted towards it by R26 however these packets are addressed to R27 The station finally receives the packets from R27 Consequently the station is busy a fraction of the time with non-useful traffic This can be improved by changing the reception and transmission operation of stations That is the station can be made to receive from any repeater along the shortest path and to transmit to the repeater nearest to the terminal that it can reach Another advantage of this type of station operation is that more repeaters can be placed in the neighborhood of the station and labeled arbitrarily These repeaters may be required for area coverage or reliability considerations Other observations of the simulation show that some terminals are blocked when the system in their neighborhood is congested and that a higher frequency of alternate routing occurs when the traffic offered to the system is increased 10 36 10 37 Network Analysis Corporation Ana'y l3 Univ-- I FIGURE 8 i 10 38 Network Analysis corporation An extensive description of the simulation program and experiments is forthcoming NAC 1974 b It is expected that the routing procedures described above will be modified as more experience is gathered Further topics to be investigated include buifer management flow control and system initialization These topics will be the subject of forthcoming reports 10 39 mmmmmii mMimm r cii¥viK ruIWI JU w» r- 7 APPENDIX AN EXAMPLE OF'REPEATER LABELING The figure below shows the set S m 1 to be labeled by S m The connection line between R eSbn l and R eS m was drawn to demonstrate that c 1 also B 3 bits f 0 v 0 0 8 4 6 S m S m 1 5 S m 0 - 7 8 9 10 11 12 13 14 15 11211322122 u V0 6 SLl 0 R 1 R 3' S m 1 0 R 4 R 10' R 15 s tim SR 0 R_ m i First label assigned is h 10 R10 «bfl«1' R 5' s Li 1 10 40 - Iim R 14' R 5' 6' V R 11' R SR 1 R m 2 R 12' R_ Rg 13 S m l 1 sJU R4 R3 R ll' R then F SMI R m l R R 12' R 6' 14' R 8 1R7t Rgt 3' R 15' The second label is h R- then F s£ 2 R m 1 V2i R2 R4 R3 S m 1 2 R 10' R n R 11' R R sr 2 $ m R 7' R 8' 14' R 15' R R 12' R 5' 6' R 13 9' m 1 ° S From now on any labeling will satisfy requirement 5 since S 2 is empty The labeling by the algorithm proceeds as fellows h 12 R 2' h 14 R 2' h„9 R- 3 h - 13 R 4 h 15 R 4' h 7 R 4' h 5 R 2' h 6 R 2' h R 8 2' The final network is 1 0 0 0 0 0 0 5 6 8 12 14 10 41 iMM MiiiimitM —„„ M a i _____ ■• j - »i - -n - 'i --i '- it - ' ■ J - iAjij - Network Analysis Corporation CHAPTER 11 COMBINATORIAL MODELS FOR ANALYSIS OF MESSAGE FLOW IN PACKET RADIO NETS 1 INTRODUCTION This report is a summary of rscent research on the macroscopic cotrjjinatorial analysis of message flow in packet radio nets We begin by developing our so-called basic model of the repeater net message origination and capture moc s The basic nodel assumes that all messages are transmitted in the direction of the fixed ground station or processing center The model is built in stages as more complex assumptions are made concerning design and operating modes of the repeater network Initially we assume an infinite repeater net at the lattice points of the usual Euclidean plane The ground station is at the origin and all messages which are repeated are accepted at each repeater Messages originate at each point in discrete time independently at each repeater according to a Poisson distribution All messages received at a repeater are received perfectly and repeated to those immediate neighbors which are one unit closer to the origin ground station Under these ideal conditions we compute in closed form the number of messages received at the ground station the number of unique messages received at the ground station and their ratio called the inefficiency of the system The next step in complexity of the model is to assume that not all messages which are received at a repeater are accepted In this case we specify two models for acceptance called Type 1 and Type 2 slotting We assume a time unit is broken into m-slots and messages received are independently and at random assigned to one of the slots In Type I slotting the number of messages accepted is given by the number cf slots with exactly one message In Type 2 slotting fie number of messages accepted is given by the number of non-empty slots Specific closed forms and asymptotic formulae are developed for Type 1 and Type 2 transfer functions the functions P - vnich are the probability that j messages are accepted given that k arrive or are received A combination theoretical-computer 11 1 imttt mmiam aw w--- ' ■ jjgjgjjjiii Network Analysis Corporation analysis is developed to obtain sample numerical data on survival of messages at the ground station as a function of various values of the parameters number of slots mean originations configuration of repeaters etc In particular probability density functions for message arrivals or receptions and acceptances are obtained and sample numerical data is given The probability distributions for the number of copies of a single message which arrive at the origin are obtained by computer analysis of a set of derived difference equations A special case of this probability distribution is the probability that at least one message gets through Numerical data are given in terms of the parameters of the model The last stage of development of the so-called basic model is to include the possibility of retransmissions when a message is wiped out Two types of retransmission modes are considered In the first mode retransmissions occur at the source of origination of the message after a time delay which depends on the distance to the origin or ground station In the second mode retransmissions occur at the point of wipeout of the message Analyses aie developed for the case of a single path from a repeater to the origin Computer programs have been written which compute and study the number of retransmissions delays and bottlenecks Some preliminary computer data has been obtained and the results are summarized in Part J of Section II To summarize the development of the basic model The basic model was developed in three major stages A Perfect Reception at all Repeaters 1 Number of messages at each repeater at each point in time 2 Number of distinct messages at each repeater at each point in time 11 2 Network Analysis Corporation B Type I and Type 2 Slotting capture model 1 Closed form calculation of transfer functions 2 3 Survival probability of messages Probability density functions of arrivals and receptions Arrivals c ad receptions at origin at each point in time Distribution of number of copies of a single message received at the origin when multiple routing is used and calculation of the probability that at least one message gets through 4 5 C Retransmissions 1 Number of retransmissions acceptance and arrivals 2 Delays and average delays 3 Bottlenecks Sections 1 through 11 summarize the advances in the basic model The items with the capital letters are the pioblems solved in each stage of development of the model All solutions are available in a computer programming package which will be described in the final section of this report In addition to the development of the so-called basic models a number of other questions and models were studied mainly concerning message explosion with multiple routing schemes The simplest such model was to assume that a single message is originated at the origin at time zero This message is transmitted perfectly to each of the four nearest neighbors each of which in turn send the message perfectly to each of their four nearest neighbors and so on For this simple scheme we develop closed form formulae for the number of messages received at each repeater at each point in time assuming an infinite grid of repeaters Some conjectures for the solution of the same problems in finite grids are made The above described simplified model was extended to assume that messages originate at each repeater according to a Poisson probability law at each point in time Questions were asked and 11 3 Network Analysis Corporation solved concerning message flow and various operating conditions of the repeaters The different operating features which were considered are i Ko message can be repeated more than k-times ii If the same message arrives from different sources only onerepeat is made iii A repeater never repeats the same message except upon initial reception iv A combination of ii and iii v A combination of i and ii Closed form solutions are obtained for each case when repeaters are in an infinite network The last type of model considered a very important part of the overall analysis of the packet radio configuration was to study the behaviour of a constant number of messages being sent to repeaters from the ground station If this model is combined with the basic model of inward flow a model for messaqes being repeated back and forth from repeater to stations and back can be obtained and studied under various operating conditions Specifically for flow of messages from the origin to the repeater we assumed that a fixed number say J messages originate at the origi i at each point in time These messages art repeated to repeaters on paths which are the duals of the input paths to the station We study how many messages get to repeaters at various distances from the ground station under the same two capture modes as we assumed for inward flow Numerical data and graphs which resulted from computer analysis of the flow equations are given The computer program is operable and can be used to develop other numerical data for a variety of combinations of values of the parameters 2 THE BASIC MODEL OUTLINE OF QUESTIONS As mentioned earlier the basic r odel for messaqes going into a ground station from a repeater network is developed in three basic stages The first and simplest stage assumes that messages are generated at each repater and repeated to repeaters one unit 11 4 Network Analysis Lorporation of distance closer to the origin Specifically Assumption 1 Repeaters are located at the corner points of a square grid depicted as follows The arrows indicate the direction of flow of messages and the lower left hand corner represents the origin or ground station Assumption 2 Starting at time t 0 and at quantized time periods afterward perhaps 1 second t 0 1 2 messages originate at each repeater independently according to a Poisson probability law That is the probability that exactly k-messages oriqinate at time e -X k X t is given by —rrr - k 0 1 2 where X is a constant which represents the mean or average number of originations Assumption 3 Allmmessages which arrive at any given repeater are repeated immediately to each repeater one unit of distance closer to the origin or ground station Problem 1 Under assumptions 1 2 3 compute X t •and X t which are defined as the number of arrivals and the number of distinct arrivals at time t respectively Note that X t and X t are random variables The quantity X t 4 X t since multiple paths to the origin will produce a multiplicity of copies of each nessage Problem 2 Compute N t and N t which are the expected or average number of messages and distinct messages which arrive at the ground station at time t Define the inefficiency of the system as the ratio N t N t Compute the inefficiency and the asymptotic inefficiency We can alter assumption 3 to model the situation where not all messages which arrive at a repeater are accepted We will 11 5 mam ■ ■ '■- _____ Network Analysis Corporation model the case of imperfect capture using two different modes For the first mode of imperfect capture which we call Mode 1 we change assumption 3 to 3 1 Assumption 3 1 Not all messages which arrrive at a repeater are captured or accepted Each repeater has the capacity to accept at most m-messages The arriving messages are independently and at random in one of m-slots The number of messages accepted is given by the number of slots with exactly one message Assumption 4 Messaqes not accepted disappear from the system Problem 3 Under the assumptions 1 2 3 1 4 compute the probability P defined as the probability that exactly j messages are accepted given that k arrive j 0 l 2 max k m The quantity P 0 for j max k m by assumption 3 1 Problem 4 Under assumptions 1 2 3 1 4 compute X t X t N t and N t Generate numerical data for a finite net of depth 00 5 repeaters in each direction for different numerical values of A and m Problem 5 Study the relationships between arrivals and acceptances at the origin An alternative model for capture is given as assumption 3 2 called Mode 2 capture Problem 6 Under assumptions 1 2 3 2 4 solve the analogues of Problems 3 4 5 The next assumption that can be altered to refine the basic model concerns what happens to messages received but not accepted We modify assumption four to allow two modes of retransmission of lost or erased messages 11 6 Network Analysis Corporation Assungtion 4 1 When a message is wiped out it is retransmitted at its source of original transmission J d units of time after its original transmission Problem 7 Under assumptions 1 2 3 1 4 1 compute the number of arrivals acceptances and retransmissions at each node or repeater for a variety of values of the parameters Carry out the same calculations under assumptions 1 2 3 2 4 1 i e change the capture mode to Mode 2 Assumption 4 2 When a message is wiped out or erased it is re- transmitted from its point of erasure one time unit after erasure Problem 8 If £ f -J • fc Problem 9 Solve Problem 7 under assumptions 1 2 3 1 4 2 and X m £ • Under the sets of assumptions 1 2 3 1 4 1 1 2 3 1 4 2 1 2 3 2 4 1 1 2 3 2 4 2 compute delays and average delays encountered by a message being repeated toward the origin 3 THE NUMBER OF MESSAGES RECEIVED AT THE GROUND STATION In this section we begin our analysis of the basic model by solving problems one two and three We study the Poisson case where messages arrive at each repeater according to a Poisson input Since our interest is in the expected number of messages arriving at each repeater under perfect capture we will assume that one message originates at each repeater at each point in time it can be shown that we multiply the resultant numbers by the mean number of Poisson arrivals To fix ideas we can plot a few time points and see by calculation how many messages arrive at each 11 7 A neiworR Analysis corporation repeater In the diagrams the lower left-hand node represents the ground station or origin Pict prially the propagation is as follows t 0 1 t 1 t 2 t 3 26 t 4 105 Let XQ t be the number of messages received at time t deterministic case 1 19 t 5 119 62 62 62 62 229 i 119 119 11 8 ■ £ Mii2Km± - j' 'L jKija 1 11«1 1 in the Network Analysis Corporation Let X t be the number of messages received at a repeater at distance d horizontal distance j i e with coordinates drj at time t We have immediatelyj X t 4 o x' t-l 1 o t l X t 2 X t-1 X2 t-1 1 O I O t and whore X2 t 2 X t-l 1 2 X t-2 2 1 2t 1-l This follows from the observation that repeaters at horizontal distance zero or d will receive the same number of messages for d 0 Repeaters with coordinates d j j l 2 d-1 will also receive the same number of messages Thus X t 2 2fc-l XoX t-l 1 o XX t-2 2t 2t 1-2 o 1 22 23 2t 1-t We conclude that Xo t 2t 3-4t-7 t 0 1 2 Thus No t the expected number of messages received is v 2t 3-4t-7 11 9 itaUatuwaMüMia Network Analysis Corporation The expected number of distinct messages received is X 2f '' 2t l Therefore No c - 2t 3-4t-7 N t 2t 2t l leff t - 4 2t 3 2t t 2 MESSAGE DISTRIBUTION WITH TYPE 1 SLOTTING We derive formulae for P the probability that j messages are received given that k messages arrive at a repeater Each message is assigned independently and at random to one of m-identicai slots The number of received messages is given by the number of sxots with To solve this problem of placing k distinct balls P is the probability that exactly one message we consider the ball in cell model into m-distinct cells The quantity exactly j cells have exactly me ball in each Let S be the set of all k-tuples where each component is one of the integers 1 2 m i e S a a2 a a € jl 2 m i 1 2 k Let A be the event subset where cell v has exactly one ball i e the subset of S of those sequences where the integer v appears exactly once Let V 2_ p Vi2 iw Sw i i 12 i i 3 w where P i i- i is the probability P A x HA-x 0 nA 1 w ' l 2 w and the sum is over all subsets of integers of size w selected from 1 2 m It is easy to compute S 3 w V 2 k k-l k-w 1 _ m k m-w w-k ITK x w k-w kl m-w » mk _ K-w 1 i i„ i w l 2 for w 1 2 min k m S 0 11 10 Ltt jtjmjäja jjllllalmitm for v min k m By the well known variation of inclusion-exclusion ik i -u- k2i - - m r 0 k-j- r J 5 l 1 ' ' ' f T n- -'-' when j min k m Actually P depends on m and should be written as P m Von-Mises has shown that when m is large P m can be approximated by X e kj l A1 j jl -k 'a Poisson variate with X e ™ -k Thia is an approximation for the binomial with p e m j q • 1-e m when k is large p small and kp moderatef - jk -k P k e m 1-e m k 3 11 11 Network Analysis Corporation 5 MESSAGE DISTRIBUTION WITH TYPE II SLOTTING t We derive formulae for P the probability that j J messages are received given that k messages arrive at a repeater Each message is assigned independently and at random to one of m-slots The number of received messages is given by the number of slots with at least one message Again we use a ball in cell model and ask for the probability that exactly j boxes are not empty when we place k distinct balls in m-distinct boxes Using the same method of inclusion-exclusion as in section B we find that m p i r-i i f -ix -£4 ki J v kj We can approximate P P k where X - X e 2 • x2 — m-j I -k is me m by the same method as Section 4 # ai-j 0 i minck m when m k are large 6 SURVIVAL OF MESSAGES Problem number three calls for the solution to the problem of finding the survival probability for a message which originates at a repeater with coordinates j d at time t We must first compute the probability that it is received at its original node Let P be the probability that a given message which arrives at a repeater is received at that repeater We must computt P under two modes or types of slotting We call P P- the values of P under type I and II slotting respectively 11 12 Network Analysis Corpomtion Let S be the set of k 1 tuples formed from the integers k 1 1 2 m Clearly n S m i e the number of elements k 1 in S is m Let P be the probability that the message is received given that k-other messrges arrive and type I slotting is used Clearly PQ 1 and for k 0 m number of elements in S with ■ in the j p position only T r m n m k m-1 lvk m which io of courso independent of timo However P is dependent on timo sinco it depends on the probability that k-other messages arrive Therefore p ° i1 t 12 k l p vK ii p exactly k other messages arrive at time t 1 In principle P t is computable from the distribution of arrivals at a given node at time t We must compute P t for type II slotting In this system the given message is received if it is selected at random from the messages in its slot °° P9 t £ P Reception k arrivals at t P k arrivals at t ' k 0 o» £ k 0 k £ P Reception k arrivals at t j in same slot j 0 p j in same slot k arrival - P k arrivals at t CO y y 1 P j in same slot k arrivals • P k arrivals 1 att k-oj-o - 11 13 » a •■„■ Network Analysis Corporation oo 1 k l m 1- 1 P2 t T k 1 k 0 t2 • P k arrivals at time t Equations 1 and 2 can be solved once the distribution of message arrivals is determined To compute the solution to the problem of survival let us for simplicity assume that the message arrives at a repeater with coordinates d d Pictorially the same problem for a repeater with coordinates 0 d 0 0 • —— - 1 1 2 2 3 3 4 4 d d Let P fdjt be the probability that a given message which originates at d d at time t is received at the fixed station at 0 0 at time t d Since the repeater at d-1 cannot tell the difference between a message arriving from d d or originating we can write P1 d t P d l t l • P message is initially received at d d The quantity P message is initially received at d d was computed as 1 and 2 in the previous analysis for type I and type II slotting Thus the survival probabilities satisfy the fundamental difference equations for P d t and P2 d t the survival probabilities for type I and type II slotting respectivejy FUNDAMENTAL DIFFERENCE EQUATIONS P d t P d-l t l of l k £ 1 m k 0 PtX t k t 0 a d l 3 with the initial condition oo PT 1 o t £ k 0 l k i-£ m „ Ptx vt k a 11 14 U i—M»__ 3a Network Analysis Corporation 0O 5 4 P2 d t P2 d-l t l E E k»0 vTT U 1 S K 1 p x t kl for t 0 d 1 with the initial condition oo 5 4A P2 O O E k r ll'i1_Ä k l1 k 0 t d - pix0yt k 4 4a 0 are Poisson with mean X For t 0 all distributions X Thus we have theoretically solved the survival probability problem in terms of the message arrival distributions We now turn our attention to the solution of problem 4 7 ' DISTRIBUTION OF ARRIVALS AND RECEPTIONS We now discuss the difficult problem of finding the dis- tribution of arrivals and receptions at each repeater at each point in time In sections 4 and 5 we have established formulae for P which connect the arrival and reception distributions It is possible to greatly simplify the problem by proving that there are only three random processes to determine A X- t arrivals at origin at time t B X t arrivals at distance d from the origin on an axis at time t C X t arrivals off the axis at time t R R R The corresponding quantities XQ t X t X t denote the reception distributions which can be obtained from the arrival distributions and P These remarks are justified by the following theorem THEOREM A P Xn t k P Xr t k U d u e each t 0 and k-0 1 2 B P Xj d t k t k P x p x„rW t -k for all pairs c Ptx R for each d e 0 for k 0 1 2 j v o d w 0 o d t kl p x o rt k for k 0 1 2 for all pairs d £ 0 and every t D P X d t k P X w t k and all pairs d w 0 and j 0 11 15 for k 0 1 2 Network Analysis Corporation PROOF The proof follows by induction on t based on the facts that all repeaters start off with the identical Poisson process the symmetry due to an unbounded region and the relationships between X D»d t and X d t Thus we need only to i termine the distributions of the random process X_ t X t are given by and X t j t 0 The initial conditions -X v k P Xn 0 k P X 0 k fi- k J - X 0 k l 0 ' d k 0 1 2 For the received randon process PlXg 0 -j P X 0 j P XR t j £ P XK 0 j I XlO k • P X 0 k — n ' Pkj PtX 0 k k j Pkj Xxk k j J k k j kl for type I slotting and V C° r -i L M k k for type II slotting k j We can substitute the formulae for P k and P k from sections 4 and 5 into this equation but the results are quite complicated The processes X t X t and XQ t are each sequences of independent random variables over time however for each repeater they depend on the values of earlier times at neighboring repeaters In fact we can write the recursive equations XQ t Y1 t-1 Y2 t-1 Y3 t-1 Y4 t-1 Y5 5 Where Y Y2 Y_ Y4 are identically distributed not independent random variables with the same distribution asX t-l and Y- is a PoisBon random variable which is independent of Y Y2 Y- Y It 11 16 Network Analysis Corporation follows that E X0 t J 4E X t-l X #■ 5a Where E denotes expectation Similarly 6 X t Wj t-1 W2 t-1 w3 Where W t-l and W2 t-1 have the same distribution as X -1 but are dependent ar d W is Poisson with mean X and independent of 1' 2 Finally xd t Z t-1 z2 t-i z3 t-i z4 where Z t-1 and Z_ t-1 have the same distribution as X R t-1 x R Z3 t-1 has the same distribution as X t-1 and depends on Z Z2 while Z is Poisson with mean X and is dependent of Z Z_ Z- There are essentially two types of repeaters in this model those on an axis and those off the axis Since neighboring repeaters have dependent arrival distributions we shall consider two types of clusters of repeaters and their associated random distributions of arrived and received messaqes x •x 1 I Ji t We define the following multivariate density functions f Y t l'Y2'Y3 p X I » 11 17 ■MS1WBB x t Y 2' 2 x t Y 3 3J 7 Network Analysis Corporation 8 f£ ZlfZ2 Z3 w PlxJ t Z1# X2 t Z2 X t «Z3 9 t Wl'W2 plx4 t siWl' X5 t W21 gt Ul'U2 plxJ t U lf X t U2 10 where x4»x5 have the distributions of X as do X X_ while Xhas the distribution of X The initial conditions are Y Y Y f Y s o i'W x x A o- - - x 2 3 WV g0 Hlfw2 ■ -2X XVW2 W I W I ' Y' Y02 Y 3 0 i' ' W i' 11 Y W 12 2' - ° Under type I slotting we can develop the following relations between the f's and g's fftZ Z Z t 1 X J V Y P Xj t -Zir X t Z2 X3 t -Z3 if Y 13 Y Y 1' 2' 3 X1 t Yl X2 t -Y2 X3 t Y3 14 • P X1 t Y1 X2 t Y2 X3 t Y3l '15 Y Y Y Z YY Y Y l'x2r 3 1 X Y 2 X l 2 Y - X-Y X-Y X Y-J 3 e 11 2 2 3 3 m X 3 X - i Y2-X2 - l Y3-X3 1-em d-e m g ulfu E W f Y l' t 1 1- e m 2'V Y rxi 16 17 PUj t ur x t -u2 x4 t wlf x5 t w2 W 1' 2 ° • P X4 t -W1r X5 t W2 11 18 18 Network Analysis Corporation W W hi 2 e - W1U1 W2U2 m W 1'W2 ° -W2 1- em -wi w rui in w2-u2 gt w1 w2 In order to determine the density functions 6 3 6 4 6 5 6 6 we need equations relacing these functions over time In generai this is a difficult task since the distribution at say X X2 refer to diagram below % °fO depends on the joint density «f Y3 Y4 Y5 Similarly the density at points along the axis depend on distributions along a wedge which increase in the number of points repeaters which must be considered o o We are thus led to define two types of joint density functions of variable numbers of random variables We define the set of all points at the same distance from the origin as an isodesic set Consecutive points on an isodesic line 11 19 Network Analysis Corporation are a sequence of points whose neighbors differ in distance by one unit from »« axis An isodesic wedge is a sequence of points on isodesic lines with a point on an axis and an equal number of points in neighboring quadrants separated by the axis isodesic weJge of 7 points isodesic line of 5 points For an isodesic line with k points at distance d define the joint density f X X P the number of messages arriving at each of the k points is X X2 X respectively Note that the order and distance are unimportant due to symmetries -R Denote the received versions by f X X Similarly for the wedge density define g X X Y Z Z is the joint density of arriving messages at time t at the points along the wedges and g X X y Z Z be the received joint densities It is easy now to write difference equations over k and time note that k d-1 otherwise f and g are not defined The initial conditions are independent over repeaters so that the joint densities are Poisson products 0 1' k — -kX e k 2 1 1 X i v v-v 11 20 i»2' k k l d-l — 15 Network Analysis Corporation k k - 4 Z Y gg X f rXjc»Y»Zjf »Z X l l •' X l k Yl 16 z l i zk' X1 Xk YrZ1 Zk 0 k 0 d-l The received and arriving versions are connected by the following equations V £t Xlf Xk rx l-em t zif' Zk Z Xj x2 l Zl o z - i Z Z 2 z 2 x2 - i d-em ••• l-em 17 2-r Y 1 Y k w X w r 0 j l 2 k - I x Y j z w 2 i 1 - - e i l Xl X2 X Z k Y Zl Z2 k -li vxi 1-e w r 2-f W 0 i l 2 k X Vxk -i R 2LT g X X Y Z Zk K tl k 1 y 0 Y - ZlXl Z2X2 ZkXk k m - i Y2-x2 d-e m -i V --' l-e1 'W l W -Z -W2 W„-Z -r £ r_v -i i_ l -S 2 2 m in l-era l-e u d-e' g Y fY«»•••»Y ir W t »W 11 21 - VZk 4in d-e 18 Network Analysis Corporation The difference equations over time are given by f X X t 1 0 W m 1 P X X W1 W X Kl 19 received at t-1 i l 2 k l P W « »Wj J l j received at t-1 so that f ti 'X-i i • « • »X 0 W m P W1 W2 Y1 X1 'P W2 W3 Y2 X2 i l 2 k l R Vi wi ''««kVW X k 2 I l i l -Xk 0 W m W -Wi-W 1 k 1 X 2 2 2 W j X cwV» «VW' ■ • • WW' i i 2 k i w w Al x 1 w 1 1 t i X K — If • • • G — L • w 20 Similarly for the wedge density functions g t x1 xk Y z1 zk 2- p Vi w FT f rV •P W2 W3 Y2 - 2J •P VWk l VV PlU k 1 Z1 S Y •p v1 v2 u1 zJ p v2 v3 u2 z2 p vk vk 1 Vzk 9 R t-l Wl ' ' rW k l'U'Vl ' 'Vi'Al' ' 11 22 m» IIWWMi' IM 21 Network Analysis Corporation EEL 0 U m o v7 0 W m w m Vwi i xi 1 i k l X x „v lh - 2k l X 2 X i 2 Z i £_ -W 1 -W k l _ m r V L Z i n-1 1 l£i£k l 3 2 A k -2 2 V j 2 3 ■ - Y ü x X - k rzi t-1 °V ' 'Wk l'u'vl' 'V'k l all divided by xrwrw2 i x2-w2-w xk-wk-wk 1 zrvrv2 i zk-vk-vk 1 Y u x - - k rzi » • Theoretically these equations can be solved since all initial condition t 0 have been' given and recurrences in time are derived 11 23 Network Analysis Corporation 8 to COMPUTER ANALYSIS WITH A CLOSED BOUNDARY The results and complexities observed in sections 3 7 indicate the usefulness of computer analysis An interesting and perhaps syrabojic special case for computer analysis might be obtained by closing the boundary at d 5 steps from the origin The distribution for each of the two modes sections 4 and 5 can be computed and used as transfer functions from arrived to received messages Of course these transfers will take place by random sampling from those distributed and hence one less type of simulation will be required The computer analysis will begin once we have numbered the 61 repeaters which lie at a distance of five or less units from the origin We do this in a counter clockwise direction beginning with d 0 d l d 2 d 3 d 4' d 5 and j coordinates 1 2 4d d 0 2 3 4 5 r as shown below in Figure 1 FIGURE 1 11 24 Network Analysis Corporation The repeaters at d 5 do not have messages arriving from other stations They only receive their own traffic at Poisson rate Repeaters at d 5 which are on the axes denoted by circles have messages arriving from the three neighbors at d 1 as well as their own Poisson traffic Repeaters off the axes at distance d 5 have input at each time point from the two neighbors at d 1 as well as their own Poisson traffic The network is activated at t 0 by having random Poisson arrivals with mean X at each of the 61 repeaters This input traffic at each repeater is converted to received messages in each of the two possible modes for different values of m by use of the transfer functions m m 2 P J min k-j m-j v 0 m V j Q -1 0 '2ZJL v m k j 0 1 2 min k m R These calculations giv us P 0 for all repeaters with coordinates d j d l 2 3 4 5 j l 4d an 0 0 the station at the origin Vie can now determine message traffic at each repeater by using equations which describe me-dsage transmission in the direction of of the origin For Time t l When d 5 j ly 2 20 the repeaters at d 5 receive only their generated Poisson traffic Thus for time 1 we generate 61 Poisson traffic numbers which describe direct i e at the source message input When d 4 the repeater at coordinates d j also receive traffic from its neighbors at further distance 11 25 Network Analysis Corporation by one unit The following equations describe messages arriving at each repeater fo arbitrary time t l On the Axis ■ F t 0 0 P U 1 t-» »U 2 t 1 P - U 3 t-l 1 4 t-l» Poi»son M_ i P1 1»P1 2'P1 3'P1 4 n DM • u l t-1 pu 2 t-1 pu 8 t-1 Polsson l 1' t 1 3 P U 2 lt-1 P 2 3 «t-1» P 4 t-l» PoiSSOn 2 4 t-1 P 2 5 t-1 PU 6 t-l PoisSOn P 1 4 t «1« P P U 6 t-1 PU 7 t-1» P 2 8 't-1» PoiSSOn P 2 l' 2 3' P 2 5' P 2 7 P 2 l lt» PU l ft-1 P 3 2 t-1 PU 12 P 2 3 t P 3 3 t-1 P 3 4 t-1 Pn t-1 tPoiSSOn R P 2 5 t PU 6 t-1 P 3 7 t-1 P 3 8 P t l2 7 At_dÜ t-l Poisson t-l Poisson P 3 9 t-1 P 3 10 t-1 P 3 ll t-l Pois£jn P3 1 P3f4 P3fV P3fl0 P 3 4 t - P ' 3 1 t P P 3 7 t 4 D t 1 P 4 2 -1 P 4 16 t-D Poisson 4 4 t-1 P 4 5 t-1 P 4 6 t-1 PoiSSOn P 4 3 t 1 P 4 9 t 1 P P 4 10 t-l Pois on 3r10 t -P 4 12 t-1 P 4 13 t-1 P 4r14 11 26 t-l Poisson Network Analysis Corporation Ä l P P 4 l t ' P P 4 5 t P P 4 9 t P P 4 13 pR 4 1 t t P 4 5 t ' 5 D P 4 9 t ' t 1 P - 5f2 P 4 13 t '' t 1 P - 5r20 t-D Poisson 5 6 t-1 P 5 5 t' 1 P 5 7 t- L Poi8Son % 10 t-1 P 5rll t-1 P% 12 t-1 Poi98On 5r15 t 1 P - 5 16 t 1 P - kl7 t-l PoiB on Off the Axes P d j P d l j t-1 PJd l j l t-1 Poisson 2'3 d d 2 3 4 P drj t P d 1 j 1 t-1 P ' W l j 2 t 1 Poisson '' j d 2 d 3 2d d 2 3 4 pR d l j 2 t-1 PU l j 3 t-1 PoiSSOn J 2d 2 3d d 2 3 4 P dfj fc P d l t 1 p d l j 4 t-1 P0iss0n J-3d 2 4d j 3 d 2 3 4 These equations relate arriving and received messages over neighboring time points and repeaters Thus the arriving number of messages can be computed in the grid at each point in time and each repeater In terms of a flow diagram the procedure for analyzing this and all finite grids follows 11 27 Network Analysis Corporation Initial Stage Compute Poisson Input at 61 pt at each point in time I Compute Tables of Transfer Functions Mode 1 randomize 1 rover distributions 4 Compute P - d o ii JJ Obtain Mode 2 P 'V 0 P d o D3 L Compute randomize over transfer functions in each mode P d t 31 Compute L_ Repeat for each point in time FIGURF 2 11 28 »e work Analysis Corporation The parameters are X mean Poisson arrival at each time point at each repeater m the number of slots in each mode one and two The output of the computer analysis is processed and presented in two forms tabular and graphical The tabular format is for each m and X mode 1 0 1 2 3 4 5 6 7 • • • • • p o o t • • • p l l t P 0 0 t p l l t P l 2 t P l 2 • • • • • • • • • • Various graphic analyses are also obtained A A graphic arrived and received messages at the origin as a function of time for various values of m and A B A frequency histogram of arrivals off the axis There are 24 points of the axis at distance 2 3 4 We take for each time t f x n imber of stations with x arrivals at time t 24 This is plotted for each time point 11 29 Network Analysis Corporation C The same histograms as in b except on the axis There are 16 points on the axes at distances 1 2 3 4 D The mean number of arrived and received messages and A x t t as a function of time on and off the axis These are given by 5 t - £ xf x x l $R t £ xfR x y l where f x if the frequency of arrivals and f x is the frequency of received messages A t £ xf x A A x l AR t £ xfAR x A A x l where f» x and f x are frequencies on the axis of arriving and received messages Some numerical results follow 8 1 Summary of Initial Computer Analysis Attached are two curves which represent a summary of data compiled from a preliminary computer investigation of a closed grid network The grid selected for initial analysis is the closed boundary grid at distance five We combined computer runs with the closed form theoretical analyses of sections 4 and 5 of this report to obtain some observations of network behaviour The first six curves represent a study of messages arriving and being received at the origin fixed ground station as a function of time We used 20 computer runs for each of the first fifty time units In this initial study the number of slots was kept fixed at 100 but X the mean number of messages originating at a given repeater was set at 10 20 and 30 All calculations were carried out for mode 1 and mode 2 11 30 Network Analysis Corporation The message flow and reception at the origin settle down at about t 4 and remained relatively constant For X 10 the number of arriving messages seemed to have a mean at about 155 and the number of received messages averaged to about 31 Since the system behaviour for A 10 m 100 settled down so quickly it seems reasonable to combine all time point data past t 10 to estimate the probability density function of arrivals and receptions at the origin in each of modes 1 and 2 when X 10 The curves would seem to indicate asymptotic Poisson behaviour with means about 31 155 in mode 1 and about 100 300 in mode 2 respectively Saturation occurs quic -iy in mode 2 for X 10 or more These results are summarized in the last four curves of probability density functions 11 31 Network Analysis Corporation CD ao- D CM- The number of arriving and received messages at the origin as a function of time Mode l o CD- - cn 10 m x 100 slots o toco C J O ao- o OJ- OH D Q 0 8 Tr 16 24 TIME FIGURE 3 32 40 1 Network Analysis Corporation o CD-i O CM- a The number of arriving and received messages at the origin as a function of time Mode 1 o CD- A m CO 20 100 slots O COCO CM o CO- o OJ- oP 0f0 c b 8 16 TIME 2 4 FIGURE 4 11 33 32 HO Nttwork Analysis Corporation O CD- zr The number of arriving and received messages at o CM3« the origin as a function of time Mode 1 X - O CD- 30 m ■ 100 slots en o CD- CO FIGURE 5 11 34 Network Analysis Corporation O 00- The number of arriving and received messages at O CM- the origin as a function of time Mode 2 X - 10 m « 100 slots O P 0 0 t 16 TIME 24 FIGURE 6 11 35 Netwoik Analysis Corporation O CD o The number of arriving and received messages at the origin as a function of time Mode-« 2 X « 20 m - 100 slots CMP 0 0 «t O en o OH CO M o OOH o rsi 0 0 t o- CD U 8 16 TIME 24 FIGURE 7 11 36 32 40 Network Analysis Corporation O The number of arriving and received messages at o rvj3 the origin as a function of time Mode 2 X - 30 P tu U t m - 100 slots ' 8 16 TIME 24 FIGURE 8 11 37 40 Network Analysis Corporation O GO O rr K i -Y O CD Density Functions Mode t A-IO 80 Messages Received 160 _ 240 UNIT ■ICURE 9 11 38 320 Messages Arriving 400 Network Analysis Corporation 3« o Probability Density Functions Mode 2 A« 0 rsi o CD •■ o n •-• •• o ftp o O o o 1«- o o c b J 80 160 UNIT 240 Messages Received 1100 Messages Arriving FIGURE 10 11 39 320 Network Analysis Corporation 9 DYNAMICS OF A SINGLE MESSAGE ON ROUTE In this section we will develop the theoretical basis for a compute analysis of the dynamics of a single message originating at a repeater in the net and attempting to reach the ground station at the origin analysis The equations derived are directed towards a computer Let us assume that the given message originates at a repeater with coordinates i j at time t If the incoming and ac- ceptance numbers at k j at time t are respectively X t and A i j X t we assume the given message is one of the X t i j i j messages Furthermore we assume that each of the X t messages i j is equally likely to be one of the accepted messages Under these assumptions it follows that at i j there are two types of messages which have arrived The first type is one message the given one the second type are X t -l messages The proba i j bility of acceptance at i j is given by the hypergeometric probability density function x ij t -i kX t -l ' x ij t 22 X t At each repeater on every path to the ground station the same analysis applies At any given repeater on the path say with coordinates k e there may be several copies of the original message which arrives Suppose k e is on a path from i j to 0 0 and the number 11 40 Network Analysis Corporation of paths from i j to k e is w Then at k e at time t plus the distance from i j to k e either 0 1 2 up to w copies of the messaqe may arrive If d is the distance from A i j to k e and at time t d X t d and X t d k e k e messages respectively arrive and are accepted then we can compute the probability that exactly Z copies of the original messages are accepted The computation of the required probabilities is a direct extension of P ex3ctly Z copies of original message is accepted at k e at time t d v copies are amongst the arrivals vwx kfe t d V k e t d -Z X X k e t d X k e t d Z 0 1 2 Equation 25 is valid at every repeater along every path from i j to 0 0 and in particular at ne origin The only ingredient needed to apply the equations to a computer analysis and generate numerical values is a formula for the probability that exactly v copies of the message arrive at each repeater This formula can be obtained recursively using the idea of isodesic line and wedge joint density functions as developed in Section 7 If a single copy of the given message is accepted at its origination repeater it is a repeated to each of two repeaters one unit closer to the origin if it is not on an axis b repeated to the one repeater one unit closer to the origin if it is on an axis 11 M Network Analysis Corporation We will focus only on a since b is essentially identical as far as the analysis is concerned The message when accepted at its origination is then repeated to repeaters at i-l j-l and i-l j Acceptances at i-l j-l and i-l j are determined according to Equation 2 3 The isodesic line joint density of receptions and acceptances are computed at i-l j-l and i-l j This joint density then determines arrivals and acceptances at i-2 j-2 i-2 j-l and i-2 j The process then continues recursively until all computations are carried out at the origin 9 1 Outline of Computer Analysis In our computer analysis we used the above results to compute the probability distributions and mean value of the number of copies accepted at the origin of a single message which originates at distance of 5 4 3 2 1 0 units from the ground station For convenience and realism of the numerical results we selected each originating repeater to have the maximum number of paths to the origin The coordinate system we used for these calculations is given in Figureil below j l 5 s S8 S6 A 7 5 1p 8 6 4 9 7 5 3 x 3 V 2V2 V r U '•r FIGURE 11 11 42 V K 'K 9 ' ■ Network Analysis Corporation The repeaters selected for originating messages at distances 5 4 3 2 1 0 are respectively at 5 4 4 3 3 3 2 2 1 1 0 0 The routes arc designated in Figure 12 and the maximum number of copies of an originating message which can be received along each repeater on the route is given in Table 1 below Note that the maximum number of possible copies is given by the number of paths from an originating repeater to the receiving repeater Note in Table 1 that no copies can be received at a repeater further from the origin than the originator 3 2 0 0 5 4 2 3 Fig 12 0 0 1 1 Routing From 5 4 to 0 0 3 4 4 3 4 4 5 4 1 6 10 1 0 3 1 4 1 2 1 3 3 6 0 1 0 0 1 0 1 0 1 1 0 2 1 3 1 0 1 1 1 2 3 1 0 0 1 0 1 1 0 1 1 2 1 0 1 1 1 0 1 I 1 0 0 1 1 1 2 2 1 2 2 2 3 3 2 3 1 1 1 1 2 1 3 3 1 0 1 1 0 2 1 0 1 1 1 0 1 1 2 2 1 2 2 2 3 3 2 3 3 3 4 4 3 4 4 1 5 4 Table 1 Maximum Number of Copies - Between Two Repeaters 11 43 Network Analysis Corporation A The Equation for ZQ j t Clearly Z j t is simply given by l j t s » a « 0 '- - V A 0 0 t ' 0 0 J XJ B j 0 1 t 0 1 2 40 24 The Equation for Z j t 1 A „ „% u j»t 25 for j 0 1 t 1 2 40 where A 1 l i 1'3 t f j -t — ' J 0 1 1 A lfl ln 0 0 t C t 0 1 2 39 The Equation for Z„ j t 26 2 n o v o 2 for j 0 1 2 2 • H ff2r x D t D 2 A -I- n __— A 1 D CM i t ——— l 2 p'j t IY ff r y t-i y 0 1 1 1 2 A 2 V ' ' D o o lu'u't t 2 3 40 where for t 1 2 39 f H-t 3 A 2 i 0 1 j 0 1 where 1 j t 2 ' t 0 1 2 38 A 2 2 0 0 t j 0 1 The Equation for Z3 j t « „« - I I fj« „t-i » W I „»0v 0 - for t 3 40 i j»t - I P- Q j A 27 t0 0 tl ' 0 0 ' j 0 1 2 3 where 1 1 I f V t-l J T - mn „ ' A 1 '2' 0 0 t ' 1 j ' A 0 0 t 1 1 1 2 V-0 11 44 Network Analysis Corporation for t 2 39 i 0 1 » 0 i «j» A 2i2 0 0 t for t 1 2 38 3 «i«'« E j 0 1 2 where 3 3 i'3 t A ' oto tT i 0 1 ' t Ä 22 10 0 « ' j 0 1 where °' l 2 37 j °' l' The Equation for Z4 j t f VJlt f p 0v 0 4 -» 7 ■»»irr 4 for t 4 5 40 12 D A 0f0 l0'°'t j 0 1 2 16 where 1 A J V 0 y 0 p 0 y-h i t 1 1 A l 2 y P j t A lf2 0 0 t for t 3 4 39 i 0 1 2 3 11 f li i tl - 1 j 0 1 2 3 where A vi i t 1 f U v -t-l $ 7 fr ' ' U 0 V 0 A p v j t -a • 0 0 t- 2 1 2 2 A 2 3 v'k t A 2f3J 0 0 t ' for t 2 3 38 i 0 1 fr 4 i 1-t -- yl fr 4 u-t 1» I»« i t U t-1 «»» l • 2 i 1 13 v 0 for t 1 2 37 f 41 -i-t _ j 0 1 2 A A A A 0 1 i t 3 2 ■ ■ — • 0 t 3 2 °' k 0 1 where 3 3 j t ■ • 3 3 °'0 t j 0 1 where A 4 3 1'3 t ti i A 4 3 0 0 t t 0 1 36 11 45 j 0 1 28 Network Analysis Corporation The numbers in Table 1 give the upper limits of the summation for the possible copies of messages which can be received at each repeater of a single message originating at a repeater further from the origin but within the net of Figure 12 With the selected net and the numbers of Table 1 we can use the re- sults of section 12 to obtain numerical data At time zero a random number of messages has arrived at each repeater To compute the distribution of copies arriving at 0 0 from 5 4 we assume one of the messages arriving at 5 4 is singled out and followed along the route using the hypergeometric analysis of section 12 The procedure was used for t -- 0 1 2 40 in conjuction with the random Poisson number generator developed and discussed earlier Specifically we seek to compute the five numbers 0 1 t 0 1 2 40 0 1 t 1 2 40 Z2 j t 0 I - 2 t 2 3 40 Z3 j t 0 1 2 3 t 3 4 40 z4 j t 0 1 2 3 4 5 6 t 4 5 6 40 Z5 j t 0 1 2 3 10 t 5 6 40 z0 j t where Z j t is the probability that exactly j copies of a message originating at a repeater at distance k at time t-k are accepted at the origin at time t For the computer analysis we considered one repeater at each of the distances as in Figure 11 The maximum j values are given by the first row of Table 1 Using the hypergeometric analyses the following equation can be used to compute each of the Z j t as a function of k 1 X mean number of originations at each repeater 2 m number of slots fixed at 100 3 Each of two capture nodes 1 and 2 For ease of notation we denote X t -w A w X t 13 13 X t -X 13 11 46 Network Analysis Corporation F 6 6 The Equation for Z5 j t t b j Z I I f p v t-l 7 A °'0 00 t for-t 5 6 40 j 0 1 2 10 where 13 3 f i j t l_ l_ I I I fj v i p t-l O p p v 0 y 0 p 0 A l 1 v i t A lfl 0 0 t A l 2 ti Pfj t A 12 0 0 t '• for t 4 5 6 39 i 0 1 2 3 4 j 0 1 2 6 where 1 2 l v y y p E i j k t 111 f' v y p t-l Y » £ J v 0 y 0 p 0 A 2 l v i t A 2fl 0 0 t A 2 2 v y j t A 2f2JC0 0 t A 2t3 y P k t A 2 3 0 0 t for t 3 38 i 0 1 j 0 1 2 3 k 0 1 2 3 where A f i j k t I I f y v t-l V J v 0 y 0 3 2 ti i t A 3 2 0 0 t A 3 3 y v j t A 33 0 0 t A 3 4 V'k t A 3f4 0 0 t ' for t 2 3 37 5 i ti ff n i j t 2 II y Q i 0 1 j 0 1 2 k 0 1 where 5 1 t A u j t t n r i fvi • A 4 3 M ff fu y t-l ' 4 4 ' 1 13 A 4f3 0 0 t A 4f4 0 0 t 11 47 Network Analysis Corporation for t « 1 2 3 36» 1 9 2 A 5 4 U jit I 0 0 t i ■ 0 1» j ■ 0 1» where t - 0 I 2 35 j - 0 1 Probability of at Least One Message Getting Threrc'i The first set of curves piguresl3-18# p3ot the probability of at least one message getting through as a function of the mean number of originations at each repeater There is one sot oh curves for each unit of distance d ranging from 0 to 5 Lach figure contains one curve for mode 1 and one curve for ir ocio 2 The number of slots was fixed at 100 The data for the curves is summarised in Table 2 below X 3 X l Mode 1 Mode 2 Mode 1 0 398 589 285 1 243 434 ' 2 355 3 X 5 Mode 2 Mode 1 Mode 2 421 264 431 192 273 1 17 321 614 166 341 129 326 428 695 164 358 119 285 4 613 874 250 534 159 271 5 740 967 341 692 157 198 distance Table 2 Probability That at Least One Message Gets Through 11 48 Nctwtnk Anatyiii Conwmlion m • o m o o o o e «o N •0 W H n e» H w 06 o e b O W 5 z ' d 00 VO in ro HonoHHi sxao aovssaw 3N0 XSV31 XV XYHX XXniHYHOHd 11 49 CM CM En Network Analysis Corporation n in O -H H « c 3 O iH N II o e -o ON 00 vo PI HonoHHJ si3D aovssaw 3N0 xsvai iv xvHi AimavaoHd 11 50 N r i f ' Network Analysis Corporation m O •H C 3 1w o s S Q O « Q O o o II e in II -0 •o CO z o H z u H H in « w tu u o o « w 2 CTl 00 £ ■■■ H9H0HHX SJ 39 3DYSS3W 3N0 isvai xv xvHX AxnifiYeotfd 11 51 N CM H Network Analysis Corporation 0 Hi 0 i 0 3 O PI o in II II 6 -0 ro ■ ■ HM H o a 1 I I vo oo I in »m HOflOHHi SX39 30VSS3W 3NO xsvsi xv XVHX 11 52 ÄxniflvaoHd fM N Network Analyst Corporation •• m II 2 O H 2 U M 05 O M CO CM O « W N ■4 Ch 100 VO If» CO HOnOHHl SI3D 30VSS3W 3N0 ISV31 IV IVJU AJillieVSOHd 11 53 fN D 2 W D « Ü - ——•SSfc Setwork Analysis Corporation W z o u u Q Q I m u ■P -P O -H H 0 C 9 o o in II II 6 TJ in II •0 Z o H oo z H W PS o O H tu O N gD Z Z -I tfi 8 1 I VD 00 I in HDnoBHX sxao acvssaw 3N0 I SV31 I V XVH1 AilliaVSOHd 11 54 ro ts Network Analysis Corporation 9# 3 Distribution of Message Explosion as a Function of Slot Size and Mean Number of Originations The equations for message explosion derived earlier in the report were used to obtain numerical data for message explosion The results of the numerical analysis follow in Tables 3 through 26 and Figures 1920 and 21 9 4 Distributions of Copies Getting Through as a Function of Slot Size and Mean Originations Tables 3-26 contain the probability distributions for the number of copies of a sirigle message which are received at the origin ground stations for each distance d 0 2 3 4 5 of origination of the message The tables vary according to mode each of two modes mean number of messages originating at each repeater A l 3 5 and each of four slot sizes m 25 50 75 100 This produces a total of 4 x 3 x 2 24 tables In table 2 7 we summarize the results of the twenty-four tables by considering only the probability that at least one copy of the message gets through s a function of distance and the three parameters mode mean and lot size Tie results of table 2 7 are presented pictorially in figures 19 20 and21 for distances of zero two and four respectively of origination of the message 11 55 Network Analysis Corporation Mode 1 X 1 m 25 distance 2 0 1 0 1 786 214 921 079 2 900 096 004 3 397 097 005 4 831 153 015 3 001 1 5 Table 3_ 25 Mode 2 X- 1 m distance 0 2 1 3 0 689 311 1 834 166 2 759 219 021 3 716 245 037 002 4 554 324 103 018 5 4 002 —■ Table 4 11 56 ■- w NsMörk Analysis Corporation I of e 1 X - 3 dit tancc o i 1 80 3 95 942 058 i 1 1 2 952 04 7 001 3 9GG 033 001 4 953 045 002 i 1 5 Table 5 Kerle 2 A 3 in 25 distance 0 739 261 1 890 102 2 887 107 006 3 4 892 101 007 826 153 019 5 able §_ 11 57 001 Network Analysis Corporation 25 Mode 1 X - 5 ra 0 1 0 813 1S7 1 2 951 963 049 036 3 4 979 977 021 022 distanced 2 001 OCI 001 5 Table 7 node 2 X 5 m 25 u ir distance 0 1 2 3 4 5 2 930 1 247 086 080 066 004 004 900 091 008 0 753 914 916 Table 8 11 58 Network Analysis Corporation i od' 1 X di stance 1 m -50 V 0 1 2 3 I 0 755 245 1 878 122 2 Si 3 6fi 001 3 796 185 019 00 1 272 v 007 4 661 l 05 5 Table 9 Mode 2 X - 1 n distanceN 0 1 2 50 3 5 i 0 605 395 1 736 264 2 602 338 060 3 531 356 103 010 4 306 360 232 083 5 Table 10 11 59 4 j 017 002 Network Analysis Corporation Mode 1 X 3 m 50 distance 0 1 2 0 783 212 1 926 074 2 921 076 003 3 926 070 006 4 882 108 009 5 Table 11 Mode 2 X 3 m 50 distonceX ' 0 1 2 0 709 291 1 860 140 2 816 170 014 3 800 178 021 001 4 875 258 058 008 5 Table 12 11 60 3 4 001 Network Analysis Corporation V QsZo 1 - 5 ui 59 oi i -r V C 'C I 734 j i 3 ' 1 937 i i j i 1 0 i 206 1 i i 063 ' -1' 057 002 954 I 044 002 j 93b 0G2 004 i 5 Table 13 Mode 2 A 5 50 distance 0 733 267 1 890 110 2 868 124 008 3 870 120 010 4 791 180 027 Table 14 5 11 61 002 Network Analysis Corporation Kode 1 1 n 0 1 o 711 289 1 831 1Ü9 2 742 235 023 3 863 269 043 002 i i 4 512 342 121 023 003 distancoX 75 4 3 2 1 i 1 5 i Ta i e 15 Kode 2 X 3 - 75 distancc 2 0 1 3 5 0 526 474 1 1 655 345 2 486 403 106 3 392 408 175 025 4 134 304 295 158 4 6 1 I i 049 00 3 001 i 5 ■ Table 16 11 62 Neto ork Analysis Corporation 75 r ou3 1 x --- 3 i r• 1 i 782 i 913 i • 2 895 891 3 4 J n 1 0 65 st-i IC6» 818 ■ 2 i 218 l1 i 087 i i t 300 i 1 103 i i 161 1 1 005 i 006 1 001 019 - j i i Table 17 Mode 2 X 3 m 75 2 0 1 0 1 674 326 815 „85 2 750 225 025 3 72 233 040 002 561 313 103 020 distance s 3 1 i I i ii i 5 Table 18 11 63 -I 002 i Network Analysis Corporation Ftoda 1 X 5 n - 75 2 0 1 0 788 212 1 929 071 2 924 074 003 3 932 065 003 4 894 j 098 008 uistanct 1 5 Table 19 Mode 2 distanced 0 X i -y_g__75 3 2 1 0 289 711 i 1 1 863 137 2 819 108 013 i 818 16 3 019 001 703 239 051 • 0 06'i i 3 1 4 is i Table 20 11 64 Network Analysis Corporation V OC G 1 c Lst vic ' 0 0 602 3 737 ■ 2 - 3 00 4 3 r 5 • 1 J ' 1 i 1 21 645 i s02 2 «n i• I 053 I 3 57 325 093 012 4 j 387 369 3 84 050 003 5 260 318 250 122 039 i 008 003 Table 21 Mode 2 distance 0 2 X 1 m 100 4 3 5 6 i 7 C 411 589 1 566 434 2 386 A ' 181 3 305 399 240 056 4 126 244 308 215 087 019 002 5 003 110 200 248 211 126 054 i • 1 Table 22 11 65 i i 1 03 4 ÜOi Network Anclysiu C-wF rGtion Mode 1 distance # X 3f m 100 2 0 1 0 715 285 1 808 192 2 834 143 02 3 3 836 147 016 4 750 5 659 3 211 • 035 004 010 26 063 4 001 Table 2 3 I'ode 2 X 3 ra 100 4 distance o 1 0 579 421 4 3 2 5 6 i 1 727 273 T 659 279 062 3 4 642 276 073 008 466 338 149 040 5 308 333 22 3 09E ablo 24 11 66 007 001 1 010 007 001 Network Analysis Corporation od 1 I i el ir Lane 1 100 X - 5 2 1 0 3 0 736 1 803 117 2 871 119 010 3 8S1 110 no« j '1 8Ü 140 018 00J 5 843 133 022 002 Table 25 Mode 2 distance X -- 5 in 2 00 0 1 3 0 569 431 1 679 321 2 674 283 043 3 715 214 064 007 4 729 16 9 076 021 00 4 i 5 802 115 056 020 005 001 4 5 i i Table 26 11 67 • o o M i IV « X I m X •o I «H ■0 in X II » o m II £ «0 1 X o o H II X i II X X o o H II X m r- i-t S 0 IN IN H IV i-t rH rH 2 4 •0 0 r 0 TJ o «c o r 10 ro IV o n H rH OH vO t m o 1 10 CO 01 rH r» m rH ■ 0 t- o O o S IV m r» r T co r IN m IV WD vO en O in r- CM IN r» in cr o 00 01 TJ 0 CM fM ■fl- rH i0 IV i m N IV n 03 rH in iC rH IV rH rH IV rH r- 0 n 00 o o IV t- 1 «» r o oi r o i-H CO H in vO O H co o «0 o o oo o m co o in r-i r-t T CO rH V O o m IN O 1 fl r m O in N 1 IV 0 vo i- t m r» n r N oo t-t X rH 0 X • 1 l r-t TJ 0 ■o 0 g • • ro ro r-t r-t • U 00 T 03 CO rH -H r CM - -l r- in 00 00 0 T3 0 N 01 T 0 t-l 0 T 0 IN • • • o t m o r r o «3 -H U 1 m r CM p 1- vO 00 00 0 Cl m 03 n ■ in f CM m V T •S » in T r-t in 00 iO rH vO 00 r o n 00 03 Cfi 10 ■ J1 T vO m o r- m n o £ r» -o f i Oi CM 10 IN in N in r 00 0 vO 03 r-t tv PO wi 01 0 £ iH rp eg rH rH 01 n 0 £ M m f V ■o rH i t ■ T N D N ff n o rH T H CM 10 VO rH rH 'S1 IN 00 rs CM O O fV o o r-i rH 10 rH „ rt TT r rH N o 4 O rH rcn en o t r ff r r- N N rH o N r f r-i 03 •o 0 s • oo 01 PO o • CM a m IV n rH 10 V rH s • o o N ■o 0 s o Tf - • -H 2 II II fr IV co o IN N 0 -0 0 X o S 10 X 0 2 m r o o H rH o 10 ro IV 01 s r IV - n II f CO 01 II IV H 0 II IT H 00 01 in N a H H H V •o o en •H IV x II in IV H f IV H r» vo 0 •0 0 X X II o» 0» H r- IV 00 1 «t m X r» tf 0« CD IN V m IN CO IV 0 TJ r- r IN 41 IV - «0 IV X ■o m H iH « r- ■ 0 m m vO r r 11 68 m Network Analysis Corporation rim f-i nm II II II II II t f r r r r CM «MM rH rH rH MODE MODE 'MODE rH w w II % % « a Q Q o in II •0 w o M rH g O H o in O « 1 Z in CM c CO VO in ro HDflOHHX SX3D 3DVSS3W 3N0 ISV31 IV XYHX AiiiiaveoHd 11 69 CN r Network Analysis Corporation i o S Ü H CM a oo r vo in 1 o HDnoHHi siaD aovssaw 3NO isvai IV lYHi xxniavaoHd 11 70 Ol Network Analysis Corporation H H N H m co m II II II o r-l ■ II •0 • CM s g3 CO o in r ü O « W fa D Z in ■ • CM o 00 o in co r-i HonoHHX sxao aovssaw 3N0 XSV3T IV iVHl AlIliaYHOHd 11 71 CM Network Analysis Corporation 10 SYSTEMS WITH RETRANSMISSIONS 10 L Retransmission Fron Source of Origination VCe now can extend the scop3 and generality of the L- ütic model by including the possibility of retransmission of ct i cj- s which are erased in random slotting or in technical lai j i _ - not captured The notion o retransmission can be c--- U c at least two ways Th» first way considered in this section that when a nessayc is wiped out it is retransmitted fro it • source of origination after a fixed delay ti 'e J d which clepc J on the distance of origination from the ground station The second type of retransmissions which we shall consider arc retransmissions which occur ai the point repeater of erasure at one time unit after wipeout The latter type will be analyzed u Section 7 To begin to develop programmable equations we v ocä seme notation Let X t be the number of messages arriving at li ' 1 i 3 u v ■ at time t which originated at u v at time t - u-i recaij that the first coordinate refers to distance from the origin Let Y t be the number of messages accented at i j J i u v at time t which originated at u v at time t - u-i Let X » t be the number of messages arrivinc at i j at do time t Let Y time t t be the number of messages accepted at i j at Let Z time t « t be the number of retransmissions at i j at 11 72 Network Analysis Corporation v 'e dcvclcD ecuaticns to compute Z have the following assumptions X t To begin we -it n tt - Poisson Variate Z t H 30 Y t X t randomised over node 1 cr node i 3 U UO 2 aistribution 31 Obviously X ij t 2X UiV t ufv el i«j 32 Where I - is the set of all repeaters which arein the input set to i j i e all repeaters for which there exists directed path to i j If we assume that each arriving message is equally likely to be accepted it follows that X t 1 3 u v 1 3 s v i j ' and that Z D ' t l—t LX u v t-J i - Y t-J i r u v in ' 3 u v i 3 v Oii'j 34 where 0 is the outward set of i j defined as the set of V 1 I J I all repeaters which receive messages from i j including i j itself The quantity J i is the delay factor which depends on i the distancefrom the origin but is independent of the source of message wipeout The only part of the equation 9 5 which is not accounted fur r„ T vi 3 a 4 t The iu v — next equation is obvious s x X i j u v t K V7 in 11 Y KfW u v t-1 35 M where II -v is the immediate input set to i j that is those vi 13 11 73 Network Analysis Corporation repeaters one unit of distance further than i j which repeat to iij in one time unit The equations 30 to 35 v ere successfully progrorjT' cd for the square grid net of repearers at the lattice points of the Euclidean plane five units or less distance iron tho origin This net has a total of 61 repeaters We do not induce nuacricc-i data fince many time points must b computed to obtain Meaning TuJ steady state results This can be done at any time since the program is available 10 2 Petransmissions at Point of Le s In this model we assume that retransmissions of wiped out messages cccur at the point of wipeout one time unit later independently of where the message originated For this type of assumption we need to compute Z s t the number oi i»3JfvU v retransmissions at i j at time t of messages which originated at u v at time s s 0 1 2 t- u-j The quantity Z is computed for repeaters u v in the input set to i j The quantities Z t and Z t are defined as in Sectior 13 Since we are assuming that retransmissions occur at the point of wipeout to compute delays we must keep track of time and place of origination of messages We therefore define the quantities x if j f u v s t ar d Y j M s t as the number of messages arriving and respectively accepted at i j at time t which originated at u v at time s According to our assumptions the required quantity can be computed from s t X v s t l'i v 1 3 u v i u v s t-1 ' - Y i 3 u v According to 5 we need to compute X anc Y which cen be done recursively Z 11 74 0 v 36 Network Analysis Corporation y ' t' - i j • J v IT l- i '• ' •■ ■' I i «•• • ' U»j •• 'v '- y 37 -i 1 V - Y s t - - Y Ct i l u v 1 3 vu- In the previous section Y ece 1 or rr o- 'o 2 distribution is X t - X 38 tl rsndoi ü • cd cv r The remaining quantity to ccrspuU t -f x 39 vV s t r U u u u v in 'l ' U'V '- II i j set These equations have been programmed for the grid of repeaters at the lattice points of the Euclidean plane as earlier The program is for the case where a repeater has a single fixed path to the origin or ground station The program was run for ten time points using a single sample at each point The numerical results are therefore subject to some variability Some of the results of a single run are given in Tables 28 - 34 As is evident from the tables saturation of the channel begins early for A 5 In Table 31 for example the probability that a message originating at d 5 at time 1 gets to the origin with a delay of less than four time units is only about 44 For X 5 the situation deteriorates rapidly with time To obtain a large set of representative data would require running the program for many time points probably at least 15 or 20 for different values of A and slot size This can be done using the available program U D ' 10 3 Delays and Average Delays as a Function of Distance We can extend the calculations and analyses described in the previous two sections to include calculations of delay distributions and average delay In addition to studying delays we can develop equations to study bottlenecks in a given network These formulae have been programmed and numerical results can be obtained Let D » t be the random variable delay of a message which i j 1 originates at i j at time t We assume that the probability that a message is delayed by k-units of time is given by the proportion of 11 75 Network Analysis Corporation Retransmissions at Point of Wipeout X 5 HflOO Model L 0 12 3 1 0 0 0 0 0 0 2 0 0 0 0 0 0 3 6 6 0 0 6 0 4 6 11 6 1 3 0 5 43 26 18 1 1 0 6 19 19 7 2 0 7 16 29 13 0 0 8 91 47 3 0 0 9 67 67 1 0 0 10 151 64 9 2 0 TABLE 28 X 5 m 100 Mode 2 0 1 2 3 4 5 1 0 0 0 0 0 0 2 0 0 0 0 0 0 3 7 2 1 0 0 0 4 4 10 1 0 2 0 5 34 20 2 2 1 0 6 37 2 1 1 0 7 19 5 0 1 0 8 28 6 4 1 1 9 33 18 1 1 0 4 0 1 1 10 TABLE 11 76 29 Network analysis Corponitkm Delay Probability Tables for a Message Being Accepted d units from the Ground Station t 5 m 100 Mode 1 Message Originating at d 5 at time 0 - dist delay 0 1 2 3 0 159 271 524 933 1 235 247 325 059 2 134 1 7 084 004 3 097 076 028 002 4 089 045 016 001 041 009 5 4 1 000 007 6 TABLE 30 A Messag«2 Origination at d 4 at time 0 v ist delay -« i 0 1 2 ° 249 454 727 1 251 221 153 2 196 123 083 3 083 070 021 4 054 033 007 5 046 018 004 016 002 6 7 002 TABLE 31 11 '7 3 1 000 4 1 000 5 1 000 Network Analysis Corporation A Message Originating at d 3 at time 0 dist dela v G 1 2 3 0 916 950 1 000 1 000 1 036 031 2 023 010 3 013 004 4 004 002 5 003 001 6 002 001 7 001 TABLE 32 A Message Originating at d 2 at time 0 N dist dela v 0 1 2 0 823 1 000 1 000 1 170 2 004 3 002 4 001 TABLE 33 j A Message Originating at d l at time 0 dist dela — 0 • 0 778 1 183 2 038 3 «JOi 1 1 000 TABLE 34 11 78 Network Analysis Corporation THE NUMBER OF MESSAGES ACCEPTED AT THE ORIGIN X 5 m 100 mode 2 Originating at d 5 at t 0 Time of Acceptance at Origin 3 messages Number Delay t 5 814 0 t 6 1 130 1 t 7 502 2 t 8 253 3 t 9 161 2 860 4 TABLE 35 Originating at d 5 at t 1 Time of Ace«jptance at Or ig in 6 messages Number Delay t 6 2 010 0 t 7 1 238 1 t 8 988 2 t 9 805 5 061 3 TABLE 36 Originating at d 5 at t - 2 Time of Acceptance at Origin 2 messages Number Del y t 7 115 0 t 8 249 1 t 9 256 620 2 TABLE 37 11 79 Network Analysis Corporation DELAY PROBABILITY TABLES FOR A MESSAGE BEING ACCEPTED d UNITS FROM THE GROUND STATION X 5 m 100 mode 2 A Message Originating at d 5 at time 0 Dist Delay 0 1 2 3 4 5 0 271 496 854 1 000 1 000 1 000 1 377 360 140 - - - 2 167 071 003 - - - 3 084 041 003 - - - 4 054 018 - - - - 007 - - 5 - TABLE 38 A Message Originating at d 4 at time 0 Dist Delay 0 1 2 3 4 0 407 452 792 1 000 1 000 1 189 300 178 - - 2 216 178 029 - - 3 092 035 001 - 4 045 020 001 - - 5 028 008 - - - 6 003 - TABLE 39 11 80 — lidMin'Maiiit - «s_w ii ■ «Jai iif iiiliii j _ j aiijiBBg Network Analysis Corporation A Mess acre Oriainatina at d 3 at time 0 Dist Delav 0 1 2 0 511 962 I 000 1 000 1 425 022 - - 2 031 009 - - 3 020 005 - - 4 007 001 - - 5 003 001 - - 6 002 - 3 TABLE 4 0 A Messacre Oricrinatinq at d 2 at time 0 Dist Delav 0 1 2 3 0 883 923 1 000 1 061 074 - 2 050 002 - 3 003 4 - - i i 5 001 - - TABLE 41 11 81 Network Analysis Corporation A Message Originating at d 1 at time 0 E St 0 1 0 800 1 000 1 191 - 2 005 - 3 004 - TABLE 42 A Message Originating at d 0 at time 0 Dist Delay 0 1 000 1 000 TABLE 43 A Messaore Originating at d 5 at time 1 Dist Delay 0 1 2 3 0 335 520 718 1 206 159 2 165 3 4 5 752 846 1 000 116 207 132 - 161 125 039 020 - 134 081 024 002 002 - 4 - 036 012 003 5 - 003 TABLE 44 11 82 ■ '■•■ ■•■ • - - - Network Analysis Corporation PROBABILITY OF ZERO DELAY VS DISTANCE OF ORIGINATION MODE 1 X 0 1 2 3 4 5 0 1 000 778 823 916 349 159 l 346 329 458 125 091 123 2 242 229 045 085 053 047 3 207 043 013 058 021 024 4 177 033 025 021 013 037 5 092 019 011 006 015 6 021 005 002 008 7 029 002 001 8 031 001 9 047 TABLE 5 11 83 ivi -i - j Network Analysis Corporation MODE 2 X 0 1 2 3 4 5 0 1 000 800 883 511 407 271 1 373 136 118 356 170 335 2 333 118 102 030 180 115 3 100 044 033 154 066 218 4 112 026 061 045 109 161 5 Co2 032 005 100 073 6 021 011 022 041 7 o045 022 019 8 005 018 9 021 TABLE 46 11 84 rtitiiHiitfiftiiih ilnifctT i Vm n „ iA i - —- - „ _ Network Analysis Corporation messages which originate at time t which are delayed by k-units If enough random samples are taken this estimate becomes quite good In notation define Y Ä» as the number of messages which 0 0 1 3 s t are accepted at the ground station at time s which originated at i j at time t Then iy irj t - ' c ft -•■ i 3 y 0 ±2 -' t •- t 40 Ihcv coLvo ccr putcr trials to dot ine 40 ever aij -ri r xütc -t' at instance i T K Cc a V r V oci rute tils e» • y d tribut ion vs - ruction oniv oi di£tc cc tc the crcur d '-La i in 1 t - i %— HD 41 t -ki where vi D 3-x D t is the randan variable delay of a message originating at eistcr ee 5 at time t To obtain a time invariant measure we can average 41 OVOJ time and obtain the probability distribution of the ra ndcn variable D and its expectation given by E D L-t k P D k 42 k o The sasie kind of analysis can be used to study bottlenecks Let D v t be the random variable delay of a message ori- li 31 ginating at i j at time t in getting w units from the ground station for w 0f 1 2 i As earlier we have P D w t k Y „ • t k i-w t -± LLL1LLA k o 1 2 ° i j t 43 where w u is the unique repeater on the path from i j to o c at distance w Similarly as in 41 and 42 P D w t k 4 L OD P D M -n w t k anc E JD t 1 V KP Di w t k 11 85 _____ 44 J — i C 5 Network Analysis Corporation 11 MESSAGES OUTWARD FROM THE ORIGIN 11 1 A Single Message Originates at the Ground Station The next major part of our study is to model the situation when message flow is outward from the origin We begin our study with the dynamics of the simple model where the repeaters are at the lattice points of the plane A single message ori- ginates at the ground station at time t 0 Every message re- ceived by a repeater is accepted and perfectly retransmitted to each of its four nearest neighbors a The number of repeaters for the first time at time t b Th e number of We determine which receive the message t 0 1 2 repeaters which have seen the single message by time t c The number of copies of the single message received by any repeater at time t The assumptions are 1 A single message arrives at a given node at time t 0 no other messages are introduced into the network We assume the message originated at the origin Cartesian coordinates 0 0 2 Message transmission is perfect i e after one time unit each of the four neighbors to any all messages transmitted by the repeater time point 11 86 ■ ■ - ''■■''' repeater ■ ■ ■ « receive at the previous Network Analysis Corporation Some diagrams and numbers are helpful to fix ideas 0 10 AQ 0 ln o o 11 iin J °— J t 1 i 1 i o 2 yf ii 0 1 0 t 0 li 2 0 V 1 40 0 a single message at each of the four neighbors no messages elsewhere TT K 0 ii l one message at origin no messages elsewhere h 4 messages at the origin 0 Message at all repeaters 1 step from origin 1 message at each of four repeaters 2 steps in either the horizontal or vertical directions 2 messages at repeaters 1 unit in horizontal direction and 1 unit in vertical yt—H Q 1 l _ direction By examining the diagrams we are led to introduce a coordinate system based on distance as measured in steps to reach a repeater and horizontal distance of the repeater from the origin The quadrant symmetry of the model also indicates use of these coordinates 11 87 iWi'nituri'rin H UHA-m-- ' ■ ■ ■■■•-■■• ■■ - '- ■'»■-■■J- - Ü 4ft i»ÖB 1f« The coordinates of a repeater are denoted by d j where d is the distance of the repeater from the origin measured in minimum time units a message needs to arrive at the repeater from the origin the second coordinate j is the horizontal distance of the repeater from the origin again measured in time units but only in the horizontal direction For example we give some coordinates f 3 0 2 0 4 2 1 0 2 1 3 2 V1 2'2 3 3 3 3 2 g 1 JUlSj 3 2 2 1 4 1'Ü • 2 1 2 0 3 1 3 0 Some further notation which is necessary B t the number of repeaters which receive the message for the first time at time t Clearly B t is the number of repeaters whose first coordinate is t i e that are at distance t from the origin A t the number of repeaters me ssage by time t which have seen the t Clearly A t C B - j 0 N t number of copies of the message received by a given repeater at coordinates d j at time t a Nd t 0 for d t b Nt d 2k l 0 for k 1 2 Thus it is necessary to compute N d 2k 11 88 Clearly k 0 1 2 A Network Analysis Corporation Calculation Of B t t The quantity B t the number of t from the origin is the number of repeaters repeaters at distance which receive the message for the first time t is easy to compute This quantity is given by the number of integer solutions to i jjl t Since a repeater is at distance d from the origin if and only if its Cartesian coordinates i j satisfy i j t we Can solve this equation and count solutions Note that i 0 j t or -t 2 solutions i-1 j t-l or -t 1 2 solutions i -l j t-l or -t 1 2 solutions i 2 j t-2 or -t 2 2 solutions i -2 i t-2 or -t 2 2 solutions i t-l j l or j -l i -t l# j l or j -l i t j 0 i -t j 0 mmummi mmmmmmmmmmmmmmmmmmammaBmmnmmmmammmmmmmmmmmmmmmmmmmmmmmmmmmMmimmmmmmmm ummmmB The number of solutions is B 0 1 B t 2 4 t-l 2 4t for t£l To compute Aft we sum B t and obtain t_ ' t t A t ZT B j 1 J 4 j 1 4 T j 1 4 t t l j 0 j l j l 2 1 2t2 2t 2t2 2t 1 The rate at which A t the number of repeaters which receive the message by time t grows as A' 11 89 t 4t 2 which is linear in t Network Analysis Corporation The quantity H d 2k K — U Xi £ B» To compute the number of copies of the message received at a repeater with coordinates d j at time d 2k k 0 1 2 we first draw some diagrams Due to symmetry it suffices to ex-unine only the first quadrant L t 0 t 2 t 1 0 0 HXk4 t 3 t 4 9 n0 K •— — i fV n o 1 ° 1 X9 36 It seems clear from the diagram that a k i i 24 o 4 L_ 30 repeater lo with coordinates d j will receive at t d the number of messages which is given by the binomial coefficient From the diagram we note the relationship of the outer edge to the d now of a Pascal triangle 1 1 1 12 1 13 3 1 14 6 4 1 1 5 1010 5 1 This result is also apparent from an argument based on the number of paths of a message from 0 0 to d j received at a repeater The number of messages with coordinates d j is given by the number of paths from 0 0 to d j which is obviously determine a general formula for N d 2k for k 1 we can write and solve the appropriate difference equation 11 90 - - -' -■•■ -• ■ ■• ■■ ■-- To Network Analysis Corporation Nd d 2k Nd d 2k-l Nd J d 2k-l Ndt1 d 2k-l NdT1 d 2k-l for k 1 2 d 0 1 2 j 0 1 2 d The initial conditions are Nd t 0 if t d Nd d d The solution to this equation is given by Nd d 2k d 2k j dk -2k To check its validity note that the initial conditions are satisfied and apply the well known definition of binomial coefficients Kd j d-1 2k Nd d l 2 k-l N 3 1 d 1 2 k-1 T1 d-l 2k _ d 2k-l d 2k-l d 2k-l d 2k-l d4 2k-lw d 2k-l wd 2k-l d 2k-lx - M k k j-l ' k-1 k j M k-1 k j-l M k k j d 2k l r d 2k-lw d 2k-l d 2k-l d 2k-l d 2k-l k k j-l k j k-1 k j k j-l _ d 2k-l wd 2k d 2k-lwd 2k 1 k M k j' k-1 M k j' _ d 2k 1 k j' r d 2k-l u k d 2k-l d 2k ' ' k-1 n k j' -d 2k k ' For k very large with respect to d we can use a Stirling approximation to note the N d 2k -2 11 91 i e grows as 2 Network Analysis Corporation To summarize a B t 4t Ol b A t 2 t B 0 1 2t l t O 4k for large k c N d 2k dk jXdk2k 2 11 2 A Fixed Number of Messages Originate at the Ground Station and Subject to Non-Capture The model of message flow from the ground station out to repeaters can be extended to alle«' the possibility of erasure ox non-capture of messages We assume that at each point of time t x messages are being generated outward from the origin Of messages accepced at each repeater a fixed proportion k hence are not repeated are a 'lressed to that repeater and o We study the distributions of the number of messages received ia accepted at each repeater at each point ir time assuming an infinite net 1 Recall X t number of messages arriving at a repeater i j with coordinates i j at time t with Mode 1 capture A 1 X t number of messages accepted at a repeater with i j coordinates i j at time t in Mode 1 capture In Mode 2 capture we use the same notation except that 1 as a superscript is replace by a 2 A In Mode One In Mode 1 capture the relationship between arriving and accepted messages is described by the transfer function 11 92 WmMUtm m mm M m maä ' ■• ■ ■ —_ — _ ' _ _ Network Analysis Corporation min k m -j when j min k m and zero otherwise We can study x t and XA ij 13 t recursively At the origin for each t 0 1 2 X t T a fixed constant ' • urthermore O min T m -w Hx V w PT 0C 'W I T m -1 vi0 v ' T-W-V m-w-V 47 If we assume T m m T-W — T L _ -1 7-r m-w-v T-V7-V if w T — v o -•'-'■' if w 48 At coordinates 1 1 1 0 the distribution of X t and X » t 1 0 1 1 are identical hence we write only X t 1 0 We have U X x t t i o xKx fe-» t X L 1 • • • jj 49 if t 0 For the acceptance at t 1 2 T P X l t j I i kj P X J p« • p x J P a o t k D 0 1 2 or recursively ■ofclilw-j o w t-1' k if Ü' otherwise 0 11 93 50 Network Analysis Corporation 1 £ Equation 50 is recursively solvable since PfX ' t-1 k is given by 48 and P is given by 46 Now more generally at a repeater at distance d with coordinates d j j 0 d We have for d 2 3 x do t - -V x d-M-i t-1 1 CM ' - 51 The acceptances are given by 2m PO$ »Cti-r - I »k r • « „ «-W 52 k r where P is given by 1 and P X J t - k can be computed recursively from kr d j 51 using the notion of isodesic line jcint densities equations for mode 2 analysis are identical except that P is replaced by P When j » 0 or d i e the repeater is on the axis at distance d a simpler analysis unfolds Since the random variables X t and X t have the d 0 d d Larr e probability distribution we write equations only for X t d 2 since d 0 — X t and X t have already been determined x dlo t - i-v x d- o t-i t d d 1 53 For the acceptances D l Ai - 0 1 2 m 54 The equations 4g through 54 can be used with computer generated data to study messaqe arrivals and acceptances at each repeater 11 94 c nim HI r naiBifcja - urtfrnuTMai'ii g m nyj ■ ' ■■ ■ ■ ■ Network Analysis Corporuiion In particular we can write equations such as 46-54 for the closed net under consideration and obtain numerical data for flow from the ground station Let X -A t be the number of messages received at i j at time t and Y » t be the number of messages accepted at i j at tine t We assume X»lo o t J a fixed constant for all tine Doints As in the inward model Y t is obtained from X-- t by randomizing over either mode 1 or mode 2 slotting I1 r J 1 When performing the calculations en the computer we assumed a finite grid of 61 repeaters as earlier However now a repeater repeats messages to those repeaters which are one unit of distance further from the origin or ground station Thus for example a repeater in a quadrant repeats to its two farther neighbors while a repeater on the axis repeats to the one repeater which is one unit further The specific equations used for the first quadrant calculations follcv we assume that -rj of those messages accepted are addressed to each repeater and hence not repeated The calculations were carried out in each of the two slotting modes Step£ 2 Set X o o t - J 80 t I 2 ' 35 ComuuLe Y o o t by randomizing over the transfer distribution in each of two modes Step 3 Compute X - t and X Step 1 X d i t Stop 4 X a 2 t - s t Y o o t-1 - IT Compute Y t and Y from 2 t in each of two modes 11 9b i in« ii -—- ■ '■-' ' - - ■ - • Network Analysis Corporation Step 5 or t 2 3 4 37 Compute X 2fl t f X 2 2 tl and X 2#3 from X 2 l t -§1 1 1 « -» X 2 2 t I Y 1 1 t-D V lf2 t-D X 2 3 t FI Y t-1 l 2 • Step 6 Compute Y 2 ■ t Y 2 izing in each slotting mode Step 7 Compute X 3 „ t X 3 3 fc » n 1 Y t 1 an 1 t 1 3 3 « lr 2 2 - » Y X X 61 2 3 Compute Y 3 2« 3 4 Step 8 3 « 'lr 2 i ' - » 3 2 2 31 Y random- X Y X Y A fc from t 1 T 2 2 - 2 3 t-1 ■L' lC t Y 3 3 t Y 4x t by randomizing in mode 1 and mode 2 Step 9 Step 10 Compute X 3 Compute Xft- 4 and Y 4 4 fc Y randomizing t from X 5 4 t -fl Y 4 3 t-1 Step 11 b Y 4f4 t-« ' Compute Y - t by randomizing and print out X's and Y's for t 1 2 40 The numerical data is summarized in Table 26 and the accompanying Figure 10 11 96 a a IM ö it- säiÄ-aajui-ui- nrrr-mh'tilUmiär Miia m Network Analysis Corporation 11 3 eosages Coming Outward i-'ro -t the Orig-P It is assumed that at each point in time eighty 80 messages originate at the origin ground station The messages are repeated outwards to the various repeaters At each point in time each repeater sends all but a fixed proportion of its accepted message to each neighboring repeater one unit of distance further from the ground station The fixed proportion not repeated is 1 61 of the number of accepted messages which are assumed to be addressed to the given repeater The number of slots is fixed at 100 In table 47 we summarize the result of this calculation by giving the average number of messages accepted and arriving as a function of distance and mode The numerical data is displayed graphically in figure 22 DISTANCE MODE 1 ARRIVING ACCEPTED MODE 2 ARRIV NG ACCEPTED 80 33 80 52 32 21 51 36 2 27 19 47 33 3 32 22 57 41 4 46 30 87 58 5 58 31 114 66 TABLE 47 11 97 iMiMiiittai—____ ___ mmmmmmmmmm Network Analysis Corporation W w u I 1 cu w u a 0 w u 0 1 H W U OS § CM CM w Q O as W Q Q S e « o s sfa fM CM gD w O u H fr z Ei W —I o saovssaw o naawnN 11 98 jj jto M g ■■VI J ■ ■- ■ ■■■ -v U i ifc fif -- - ■ ■ „-Ü i ■ ■ ■■ •-■■ •' - i - - ■■■■ Network Analysis Corpomtion 12 OTHER MODELS A number of models other than the basic model were consi- dered The results for quantities of interest were obtained in closed forms under the assumption of an infinite grid ample of such a model was described in Section 3 messages repeated only toward the ground station that was part of our basic model the results of Section 3 One exfor Of course In the process of developing we assumed that a single message originated at each repeater at each point in time and multiplied the resuJts by the mean T to obtain average flows We will now justify that calculation and study uninhibited passage of messages in each direction in an infinite grid Our new assump- tions are 1 At each point in time starting at t 0 messages originate at each repeater according to a Poisson distribution with mean X• 2 The arrivals originations at each repeater are independent over time and different repeaters The probability that exactly j new messages originate at any time point at any repeater is V j j j 0 1 2 We compute formulas for a N t average number of messages which arrive at the origin at time t Since all repeaters are statistically identical there is no loss in generality in studying message flow at the origin j t ■ -■ -—- ■ —- - — Network Analysis Corporation b N' t Average number of distinct messages which arrive at the origin at time t for the fust time c Ieff t Inefficiency of the network defined by average number of messages average number of new messages for the 1st tine No t leff t „ t This is a measure of inefficiency since the larger Ieff the more inefficient the system The actual number of messages which arrive at the origin at time t is a random variable In fact it is a sum of a large number when t is fairly large of independent random variables The summand random variables can loosely be described as the contribution to message flow at the origin arising out of some number of messages originating at each repeater at each point in time To compute N t we can sum up all the contributions» is interesting but tedious This A simpler method is to compute X t which we define as the number of messages arriving at the origin at time t in a deterministic model obtained by assuming that at each point in time at each message originates repeater exactly one new It will then follow that t K 1 0 t Similarly if we define X t to be the number of distinct messages that arrive at the origin at time t in the deterministic model it will follow that N'0 t Nx0 t We indicate an armwaving proof of the first assertion The quantity No t is a sum of average contribution to the flow at 11 100 ■MüMtaa u jdl mm Network Analysis Corporation the origin at time t as a result of messages originating at repeaters less than than t t units in distance and times earlier The average contribution from each repeater is a constant not with time at each fixed time point and repeater multiplied by X the average generation rate the constant is given by the calculations in section II and depends on the coordinates d j and time Thus X factors from the sum and N0 t isXmuitiplied by the total flow resulting from a single message originating at each repeater at each point in time Ke now make the specific assumption At each point in time and at each repeater a single new message is originated Under this model to compute X t and hence N t is trivial To fix ideas we depict the situation at three time points t 0 At time zero one message originates at each repeater hence the message flow is X 0 1 5 H—V t l 51 k 11 101 ■■■■■ -w - - 1 i ti Network Analysis Corporation At time 1 each repeater receives 5 messages one from each of four nearest neighbors and one new message 21 21 t 2 21 k At time w 2 each each of its 21 repeater receives 5 messages from four nearest neighbors and one new message for a total of 21 To compute X t in general we note that each repeater is statistically identical in terms of message flow XQ t 4X0 t-l 1 Hence t l Xo 0 1 This difference equation is trivial to solve and hence XQ t 4t 1-l t 0 Thus NQ t 4t l_1 To compute N ' t we consider the same deterministic model o and compute X ' t the number of distinct messages which arrive at the origin for the first time at time t It is easy to com- pute X' t from the following table by summing contributions 11 102 nin nm ■•'• ViüMii'Jtahii' v' if'B'iL -IX—I_LL Network Analysis Corporation Time of Origination Distance from Origin Number of Messages 0 t 4t 1 t-1 4 t-l 2 t-2 4 t-2 t-i i 4 t 0 1 The first column is the time the message first appeared in the system if it is received by the origin for the first time at time t The second column indicates the distance from the origin that the message originated The third column indicates the number of message originated at that time and distance which are received at the origin at time t X t 4t 4 t-1 2 2t 2t 1 Thus t 4 1 27 4j l j 1 O 0 Thus NJ t 2t2 2t 1 The inefficiency of this undamped network is leff t J t l j _ X 2t2 2t l 4t l-1 4t l 3 2t2 2t l 6t2 The inefficiency grows rapidly with time for this undamped system 11 103 iüüiii i iiMiMi ii i iiiiiiiiii iiiiillü'Üli Network Analysis Corporation We can now put restrictions on the operating characteristics of the repeaters and message flow 12 1 Ho Message Can Be Transmitted More Than k Tiroes In this mode it is assumed that each message has a counting feature whereby each time the message is is updated by one unit repeated the counter When the counter reaches the number k the message is no longer repeated and disappears from the system In this mode we compute a NQ t average number of messages received by the origin at time t b N' t average number of distinct messages received at the origin for the first time at time t Ieff t Hui No t Once again by the argument presented in the previous section it suffices to consider the deterministic model and tj compute X t and X t To fix ideas we diagram the first 6 time points inherently assuming k- 5 11 104 r i ITU ■ _ _ ammmatM Network Analysis Corporation t 0 one message at each repeater all of age zero five messages each repeater one of age zero four of age one t 1 21 messages at each repeater 1 of age zero 4 of age one 16 of age two 21 21 85 messages at each repeater 64 of age three 16 of age two 4 of age one 1 of age zero t 3 341 messages at each repeater 341 256 64 16 4 1 t 4 341 341 11 105 ■MÜMI imjftamigng of of of of of age age age age age four three two one zero Network Analysis Corporation 1365 Messages 1024 t 5 1365 13f b 1365 1365 256 64 16 4 1 1365 of age 5 of of of of of age age age age age 4 3 2 1 0 TOTAL Let X k t be the number of messages arriving at the origin at time t whose age is less than k transmitted That is those that will be Since the flow at all repeaters is statistically identical XQ t 4X k t-l 1 1 The number of messages received at the origin at Lime t is four times the number that will be transmitted by any of the four nearest neighbors plus one new one Once again this is trivial difference equation to solve in k We obtain as a solution k 1 4 k l i xo t - 1 t£ k 4t 1-l xo t 1 -i t£k Hence by the arguments above 'M±k 1-i tik NQ t t k 11 106 ammmmmmm Network Analysis Corporation » similar analysis shows that N0 t J2k2 2k 1 t k 2t2 2t 1 tfik Thus Ieff t -A 4k 1-l A 2k t k 2t 1 k l 2-4 4k 1-l 3k2 3 2k 2k 1 6k In tabular form for k l 2 3 4 5 the inefficiencies are given 3 40 22 4 8 3 Ieff 1 62 12 2 If the Same Message Arrives From Different Sources Only one Transmission is Hade In this mode of operation a repeater has the ability tc compare messages which arrive at the same instant We may consider this mode to be a memory type system of length of time one unit or instantaneous toe seek to compute N t and 17' t consider the deterministic model Again we To fix ideas let us examine some early time points and compute multiplicities Ail re- peaters in this case also have statistically identical flows 5 t 0 1 t 1 21 t 2 21 ► 21 11 107 iTiiliiliiiiiiliÜMMMMHiil iiMMiBiiiWimfciiiiiii-ii MmtmttHä i__i_ i ■■■' - ■■- - «- -- ' - Network Analysis Corporation At time t 2 all repeaters statistically identical receive 21 messages and they are Of the 21 total messages received at the origin only 14 are distinct We can partition this total using a table as follows Origin of Message Number Distinct Time of Origin 0 0 t 2 1 1 1 1 0 t l 4 2 0 2 1 2 2 t 0 8 0 0 t 0 1 The total distinct is 14 Hence the diagram for t 3 iS t 3 of the 57 57 4 14 1 one is new and 14 came from each of four nearest neighbors The same method can be used to compute Xj 2t and XQ 2t-l in general Let X 2t and X 2t-l be the number of distinct messages received at the origin at time 2t and 2t-l respectively Clearly these quantities satisfy XQ 2t 4X 2t-l 1 and X 2t l 4X 2t 1 Thus it suffices to compute XQ 2t and XQ 2t-l 11 108 ■witeii iii ma »»A „ j j in fr tlfl 1 j Network Analysis Corporation To compute X 2t and X 2t-l we decompose each as follows o o #1 2 3 t 1 xjO 2t X ' 2t X ' 2t xj' 2t O O Of XdO 2t X '1 2t-1 X 2t-1 Where X x£'2 2t-l X 'fc 2t-1 # v t number of distinct messages received at the origin at time t for the v time The quantities X ' t are computed by the following table which essentially decomposes X ' t by distance and time of origination of each message contributing to Xd V t For Xd 2t-1 st _ time of origin Oil i mmmmmm dist at origin 2t-lg2t-2 » 2nd mmmmmmmm • 2t-2 j2t-l _ time of origin I 0 8 1 I ' dist of originm-3l 2t-41 » » » J2t-4 J2t-3 I 1 I 0 t-l thtime- Time of origin JO j 1 2 j 3J ' dist at origin 3 12 1 1 I of t ' time - time of origin I 0 1 1 dist at origin 3 1 j 0 The grand sum is 2t-l XJ'VL 4 X 2t-j j l 7 2t-l X°'z- 1 4 21 2t»j ° j 3 2t-l d fc X ' 4 2t-j • ' o j 2t-l since the number of message s originating at distance d is 4d as we have seen earlier Therefore „a t 2t-l 2t-j 2t-l t 4 k l j 2k-l 11 109 tt mün iMIfii - -»' 'tin n HI— - i •■■■■ -■ - Network Analysis Corporation After summing we obtain xd 2t_1 m tut inatii By a similar analysis we can show that Xd 2t 4t 3 2t l t 1 ° 3 Thus X 2t 4'xd 2t-l 1 4t 4t l 2t l 1 o o 3 x 2t 4t»3 8t» » J o Similarly X 2t l 4-Xd 2t 1 4 4t 3 2t l t 1 3 x 32t3 72t2 52t 15 Hence N 2t 2 X 4t 3 8t l N 2t l y 32t3 72t2 52t 15 ° 3 NX 2t 2t2 2t l 8t2 4t l The efficiency of this mode is Mf 2t 4i±3H8t ilI_4t 3 8t 4t l 3 11 110 ° ■■ ■-- -■ A ■■'j» or Network Analysis Corporation 12 3 A Repeater Never Transmits The Same Message More Than Once Except Upon Initial Reception This mode of operation implies infinite but not instantaneous memory in the repeater We analyze the deterministic case with no loss of generality Pictorially the first few time points appear as follows t 0 t 2 t 1 21 Of the 21 messages received at t 2 there are 17 which are received for the first time These can be enumerated by point and time of origin 1 new one at t 2 d 0 f 4 at t l d -l 12 at t 0 d 2i- Thus there will be 69 messages received at each repeater at t 3 In general let X o t be the number of messages received at the origin at time t 3 and X t be the number of messages received at the origin for the first time at time t Then XQ t 4 X t-l 1 11 111 ■ »■■■ ■■ ■ '■■■■- ■ ■ Network Analysis Corporation If a message was received for the first time at any repeater at time t-1 it originated at distance t-1 at time 0 or at d t-2 at time 1 or at distance 0 at time t-1 Summing these by their appropriate multiplicities we obtain xi t-i ° s t_ou 1 t_- 1 1 M k 2 j 0 J X1 t-1 2t 2-4t-3 Xo t 2t 4-16t-ll ' and f Similarly No t 2t 4-16t-ll and as before N J t 2t2 2t l The efficiency of this mode is „ _ No ft _ 2t 4-16t-ll No1 t 2t 2t l 2t 3 tZ 11 112 Igj ggjfr jgffifrg mmtu - -m 1 jr iil r i- -- i■ J frMMfttt - V ■ '- '■ LlJA iWWjäli -j Network Analysis Corporation 12 4 Mixture of Modes 12 2and 12 3 In this mixed mode a repeater has infinite memory for comparison of messages and instant memory The result operational of this mixed mode is that when multiple reception of the same message is received only one transmission is made Furthermore if a message is received for the second time it is not transmitted at all The result of this combined mode is to reduce the transmission in the instantaneous mode to only messages received for the first time Therefore XQ t 4Xo'd t-l 1 where X • f d t is the number of distinct messages received at the origin for the first time at time t This quantity has been previously computed to be x' d t-l 2 t-l 2 2 t-l 1 2t2 - 2t - 1 It follows that X o t 8t2-8t-3 ' and NQ t A 8t2-8t-3 The efficiency of this mixed mode is seen to be 2 n 0 n 2 Eff t - vt8t -8t-3 8t«-8t-3 4 A 2t 2t l 2t 2t l 11 113 1 __ j- LiLBiU - j-il j _ _ _ Network Analysis Corporation 12 5 Mixture of Modes 12 land 12 2 In this mixture of modes no message can be transmitted more than k-times and each repeater has instantaneous memory but not finite memory This mode also provides an upper bound to the case where each repeater has zero capture and messages are dropped after k transmissions k little analysis will show that for t k there is no change in the message flow from the instantaneous memory case For t k the exact same analysis as in the instantaneous memory only case shows that the formulas are exactly those except that t should be replaced by k Therefore in this mixed mode for memory of k 2k 3 8k2 l S O k A 2t 3 8t2 l XQ 2tM t kj 32k3 72k2 52k 15 t k 32t3 72t2 52t 15 t k Furthermore No 2t XQ 2t N 2t l - X 2t l o o We arrive at the same result with t replaced by k lEff 2t 2 14k 3 4k l 4k 3 8k 4k l In tabular form Eff k 1 33 1 2 67 2 4 0 3 5 3 4 6 67 5 8 0 6 11 114 mmatmmmsi ■ - ■ t in M - • ■■'■'-■ Network Analysis Corporation 12 6 A Closed Boundary Model In this part of the model it is assumed that each repeater is less than B units from the origin units are measured in steps As in earlier cases the The region is now closed and ap- pears as follows Furthermore in the initial stages of this model it is assumed that a single message originates at the origin at time t 0 All message flow is generated as a result of this single message Unfortunately this model causes a loss of symmetries which facilitated the ease of obtaining closed form solutions for message flow in the previous models ever some closed form analysis can be obtained How- In particular it is not difficult to obtain an algorithm which will supply a complete analysis of message flow at any point in time on any repeater or station Let N° 2t d be the number of messages received at a station or repeater which is d-units from the origin and j-units from the y-axis at time 2t d where d 0 1 2 B-1 j 0 1 2 11 115 ältmmmmm Mama » - „■ ■» „■■ ■■ B Network Analysis Corporation The equations for N 2t d are identical to the equations for the open boundary case when 0- t -B-d since the closing of the boundary does not affect message flow at a repeater at distance B-d until t B d d N B ut a Therefore i nl u t § We can use this equation to compute message flow at all time points up to and including t B To compute message flow after time B we can work backwards from the boundary and successively compute message flow at each station or repeater for any time point using the equation we will develop however it First is helpful to examine a particular case with a diagram and compare the closed boundary with the open boundary We let B 4 Closed Boundary at B 4 Open Boundary The closing of the boundary will not affect any repeaters or stations until t 6 t 0 t l t 2 t 3 11 116 ■ - —■■ ■■■■ ■ - ■ 111 - o t 4 t 5 t 6 t 7 1225 0 400 1100 0 SwX 3025 Xl400 400 t 8 VsK 4900 vX° 400 0 3025 0 0 3136 0 It is obvious hcv to continue for as long as one wishes to obtain the message flow Since all message flow can be computed by the formulas of the proceed- r - section for t B the message flow with closed boundary can bo computed by backward for all times larger than B The initial conditions at time t B are given by the following relations At time fc B i B 1 if B 2k a otherwise 11 117 IhHriMfeaK - LtMf »w iteration Network Analysis Corporation since N B is zero unless B and d are both odd or even numbers At time t B l S B B 1 0 i e no messages at the boundary »3 B 1» B 1 N° B l r k Mk j ' if B 2k d-l B J I 0 otherwise At time t B 2 On the boundary N l B B 2 - N B 2 1 J j'B i j-i B i BB1 l' 5 B-J B 2' for j l 2 B-1 for d B B 2 B 2 N£ if B 2k d-2 B 2 j 0 I 2 otherwise At time t B 3 On the boundary NB B 3 0 B r3 j 0 1 2 B At distance d B-l B 3 U N B 2 1 O B B 1 B B2 2 N 4 i B 2 B 3 B-I 11 118 muimmmm 2 2 B 2 1 O - d Network Analysis Corporation MJ CB 3 N 2_I B 2 N 1 B 2 N 2 B 2 N B 2 0 ■ B 2» - Ti-n«» « j—1 2 B—2 At distance d B-l B 3wB 3 N° B 3 l k Mk j' B 2k d-3 j 0 1 d otherwise At time t B 4 On the boundary 2 2 BnB1 BR B N B 0 B 4 u B 3 N B 4 1 I N r B 4 B B i B 3 B 3 - S £ Note that N N B 4 must be computed separately since B i N B 3 and N ' B 3 for j 1 do not share a common formula i e are not special cases of a general formula NBtJ B 4 NB_1 B 3 NB_1 B 3 B -l b J Note the formula is the same for j l as above j 2 B- 2 At distance d B-2 K B 4 I O o B 31 J B 3 2 «I 1 10 » - » ♦ B 2 ♦ B B3n2 2_2 B 11 119 Network Analysis Corporation B 4 J - NB J-I B 3 N B 3 B J I N B 3 B J NB 3 B 3 - c nn1» E 2 B' B 3 B »' ■ l-i-2l l for d B-2 4 v d B 4 „ r B - N k k 3' B I »J if B»2k d-4 0 otherwise At time t B 5 at distance d B-l N B 5 B O N B 0 B 4 « 2 V NB B 5 NB 2 B 4 N B 4 B O 2 B B2 2 H B l B 4 BB3 2 N _l B 5 NBf2 B 4 NB 2 B 4 NBa B 4 i2 j1 2 B 2 B i H B 5 NJ-2_I B 4 NB j 1 B 4 NB 2 B 4 NB B 4 Bf D u V B 2 N - B 5 B B-J-I j 2 B—3 11 120 X- B B3»i Network Analysis Corporation At distance B-3 N B 5 B O N B 4 J N B J B 4 B O O B 2 B 3 2N B 4 B I Cn2 NB 3_3 B 5 NB 4 B 4 NB 2 B 4 Bf3 BfJ _ B 5W B 1 - j 4 K B B 2 B B 3 B 3 4 B j l 2 B-4 B-j-3 B 5 for d B-3 B 5 l B 5 Ng B 5 j k k j if B 2k d-5 0 otherwise j 0 1 2 fd We will continue for three more time poin s to get some idea as to how the solution behrveswith time We will omit the general equations and give only the results since it is clear that the expressions become too cumbersome for easy comprehension For time t B-i-6 at the boundary i 5 _ B 6 2 B 2 Bt2 Bt3 2 B B 0 B HJ#1 B 6 i2 B 1 B 2 B 2 2 li 121 N B B B 6 B 3 3 B B 2 3 2 B V B 4 Network Analysis Corporation 1 B 2 B «iB 2 B 6 i2cB« ♦ 2 B B2 ♦ c8 3 0 B t---- « B ♦ B N - - r-wB l B B 6 2 a - B 2 t j 2 B B 3 U B 6n v « B '' J 'l VT T' J 3' ' j 3r 4 B-3 At distance d B-2 HB 6 U V ♦ 3 B 2 ♦ 2 « ♦ B B4»l2 - L2 B 6 NB 2l B 6 13 B« ♦ 3 B 2 ♦ 2 B 3 ♦ B 4 B B1 NB 2 B 6 - B« B B2 B BS 1 HB-2_3 B 6 3 ™ 3 B 2 2C™ ♦ B B4' B 2 j B S j 2 B-4 At distance d B-4 C-V N B-4 B 6 B J B2 ♦ • •♦ «B B5 2 - «_4 »6 B 6 B 1 B 2 » T 4 2 B 5 T --- „B-4 N T - S i-4-i B 6 j l f 2 B—5 For d B-4 B 6 B 6 N° B 6 j k' k j' if B 2k d-6 otherwise At time t B 7 At distance d B-l J B 7 U 3 1 ♦ MBB2 11 122 3 ♦ V 2 - £_ »» Network Analysis Corporation £ « 5 1 B 1 I«T N 5 B J 8 3 » 3 B 3 ' ' Bv - BiB5 B B 2 B » B 7 B B-2 B-l N B 7 -tfei 5 B 1 5 B 2 3 B 3 TV B 4n B ' B N£J_ B 7 B-1 _ B 7Wc B lx 5 B 2V 3- B 3X B '8 7' - 4 '5 B ' B 4 B » ♦ IT - B j 3 B-4 At distance d B-3 NB B 7 - 4 B« ♦ 4 B 2 N B 7 NB 3 B 7 3 B« 2 B 4 4 I8« 2 B B - 3E B 4 V 4 B« 3 B 3 2 B 4 B 5 B ■ B 4 B 1 B 2 3 ' 5»I B ' B » J B 3 2 ' B » B 4 ' •••fj3 ™Ji At_distance B-5 N B B 7 E« 2 y7» - l B 7 £ B J B 7 1-1 2 At dAB-5 N°B B 7 '3 tK ' i- k j 0 if B 2k d-7 otherwise 11 123 B 5 B » B » B-6 Ne'work Analysis Corporation At time t B 8 at the boundary 5 B 1 5 B 2 3 B 3 B 4 2 N 0 B 8 N B B 8 NB l B 8 5 B 5 3 B 1 B B 2 B 2 B 3 B 4 B 2 B 5 1 • 9 9 6 3 Y B B N f2 B 8 5 B V5 B 3 B 3 B 4 • 5 BB2 4C 3'BB4 2 BB5 BB6 NB 3 B 8 d B 5 B l 5 BJ2 3 BJ3 B 4 NB j B 8 JfS 1 2 3 4 j 4 B-4 At distance d B-2 NB 2 B 8 t9 B 9 B 2 6 BJ3 3 4 B 5 2 NB 2 B 8 - 9 B 1 J-9 BJ2 6 B 3 3 B 5 • s B 1 5 B 2 4 B 3 3 B 4 2 B 5 Y B 2 B j B 1 B 2 N B 8 g 9 J 9 6 B 3 3 B 4 B B5 MS7 CB 8 - BJ8 t9 B 1 9 B 2 6 B B i 3 B 4 t B 5n 11 124 Network Analysis Corporation At distance d B-4 H£J B 8 tS 1 « 2 3 « 4 « 5 6 2 B-4 B 8 l B 8 B k l w - 5 B« « B 2 4 B« 3 B 4 2 B 5 B 6 j 2 B-6 At distance d B-4 if B 2k d-8 B 8 -« « » « otherwise This completes an analysis of the first eight time points past the time to the boundary The expressions are quite unwieldy However the algorithm is clear and can compute message distribution throughout the grid at any time point We write down the general set of equations and then indicate a closed form combinatorial method to make sense out of the unwieldy expressions The General Equations The initial conditions for t B are At time t B Initial Conditions 4#j B j k k j if B 2k d otherwise 11 125 Network Analysis Corporation The General Equations Cn the boundary k 1 1 N 0 B42k N B B 2k NB J B 2k-l 2 NB B B 2k »3 N® hB 2k-l ul B »D 0 3-1 B 2k-l j —1 2 B—1 Note that B NB B 2k -Hj B j—0 B IH2k fl Along the axes 0 d B k l 2 N B o B 2k - a£o B 2k-1 N B J B 2k-1 2N - B 2k-l Ö l N B d B 2k Off the axes 0 d B 0 j d N B 2k I ö 1 B 2k-l N d_1 B 2k-l B D fD 3 NJ'J B 2k-l NJJ J B 2k-l At the origin N° 0 B 2k - 4Ng 1 3 2k-l This completes the general equations A Conjecture on Solutions to the General Equation An examination of the coefficients of the D expressions in the first eight time points indicates that the coefficients 11 126 Network Analysis Corporation are the same as the rows in the following infinite sequence of tableaus i k l k 2 k 3 k 4 k 5 k 6 j l 2 1 1 2 5 14 42 1 2 5 14 42 4 3 1 3 9 28 5 1 4 14 1 2 3 4 5 6 1 5 0 1 3 9 28 90 1 1 3 9 28 90 1 2 6 19 62 T k l 2 3 4 5 6 0 0 1 1 1 1 4 4 3 14 14 10 48 48 34 165 165 116 1 3 10 34 1 4 15 1 5 T 1 2 6 20 69 j 3 10 35 1 4 15 1 5 1 0 0 0 1 1 1 4 5 5 20 20 15 75 75 55 275 275 200 4 1 1 1 3 2 1 10 6 3 1 35 20 10 4 125 70 35 15 1 The tableaus through T cover all the coefficients which arise up to and including t B 8 It is possible to give a solution for S T which is the Jj element in the k row kj » of the tableau T„f v 1 2 However it is perhaps not obvious how these tableaus are generated The j term of the A 1_ k row of any tableau is obtained by summing the last k p-j terms in the previous row That is the third term in the fourth row of T is obtained by summing the last three terms of the third row 1 In mathematical form the equation for the tableaus are Initial Condition S - V 0 j 11 127 1 5 1 Network Analysis Corporation k-n -2 S S k l V k 2 V - £ Sk-l J V3 1 k v-2 V w j-l £ A 'w V It is clear that the between tableau equations are S k j V «V S k j Tr l - Vl j TH-2' ' k 1 ' X 2 '- S k l j Tl Sjcj ' Thus to solve these equations it suffices to give a general formula for S recursively T The other terms can then be computed It is easy to check that the solution for T is given by s k j Tl 4 2W ' J-1'2 k Then by recursion T Ji 2k j 1 _ if 2 - 1 k jU2 k ll k k k-1 '' S b K X k l ' — T X j s T3 2 ' £ f m • j K ' 'Xi 2k J 3 i 2kr3 1 To apply these results we take a particular example to conjecture N Q B 2k lESki iT1 2 ry • i 2 if k - -1M B 3 J2 k-l B ' 11 121 f fc21 Network Analysis Corporation This conjecture holds for time points k l 2 3 4 k 1 This conjecture holds for all k l 2 3 and satisfies the general equations 11 129 Network Analysis Corporation 13 SUMMARY OF RESULTS OF THEORETICAL MODELS Recall that N t expected number of messages received at the origin at time t N o t expected number of distinct messages received at the origin for the first time at time t Eff t H t o N' t These symbols are in the model where there is at each A repeater at each time point Poisson input In all modes N« t 2t2 2t l o Deterministic The first model analyzed is the effect of a single message originally at the origin at time zero messages ever enter the system Wo other The prop gation of this message can be measured by the following turee quantities 1 Bf - - the number of repeaters which receive the message for the 1st time at time t B t 4t for t lr 2 i A t the number of B 0 1 repeaters which have received the message by time t» 3 at a — ' M —■— A t 2t' 2t l N t number of copies of the message received at time t rrpeat er with coordinates d j 11 130 Network Analysis Corporation if Nj t 0 t d KfJ d j Nd d 2k l — J K—0 1 2 x d 2k Nd d 2k d 2k k k » ik 0 A 1 1j The quantity N d 2k can be more generally interpreted as the number of copies of a message received at a repeater which is at distance d and horizontal distance j from the originating repeater after d 2k time units B Poisson Input Results 1 With no restrictions imposed on the operation of any repeater N t o 4t 1-l N' t fc 2t2 2t l t 1 -l Eff t 4 3 2c 2t l 2 ri 6t No Message Can Be Transmitted More Than k-Times N t o A 4k -1 N' t A 2k2 2k l k 1 Eff t 3 2k 2k l Eff I 1 11 60 I 3 401 8 3 I 22 4 11 131 Network Analysis Corporation 3 If the Same Message Arrives From Different Sources Only One Transmission is Made This mode of operation assumes that a repeater can compare all messages arriving £t the some time and transmit only one copy of duplicate messages It is inherently assumed in this mode that there is only instantaneous memory which we may call 0-memory 2t N X 4t 3 8t'- -l N' 2t A 8t 4t l p IEff 2t HSt l 3 8t 4t l 4t This mode produces a substantial reduction in duplicate traffic 4 A11 Messages Are Transmitted in the Direction of n Fixed Ground Station In this mode it is assumed that repeater knows where the message should be received This mode is better than no mode but holds little promise by itself 5 A Repeater Never Transmits The Same Message More Than Once Lxcept Upon Initial Reception 11 132 Network Analysis Corporation In this mode a repeater has infinite memory but not instantaneous memory ■ t x 2tT -u N' t X 2t 2t l o t 4 IEff t 22 - -16t-ll -16t 11 2t 2t l 22t i t It appears that infinite memory without instant memory does not damp the message flow significantly in fact it is worse than directionality in the repeater 6 Infinite Memory Plus Instant Memory If we combine the two modes of operation NQ t X 8t'-8t-3 N'o t X 2t 2t l Eff t 8t -8t-3 The efiect of combining the instant memory feature with the insbantaneous memory feature is to reduce the message flow in the instantaneous mode by a factor of t 3 which is significant 7 Instant Memory Plus no Message Transmitted More Than k-Times In this mixed mode the analysis shows that all results in the instant memory case are the same except that the flow becomes independent of time after t k Eff t k lEff 1 33 The inefficiency is 2 67 11 133 5 33 I 6 67 18 Network Analysis Corporation CHAPTER 12 TIME AND SPACE CAPTURE IN SPREAD SPECTRUM RANDOM ACCESS I INTRODUCTION AND SUMMARY When a receiving station for packet data communication is being accessed in a random access mode the use of spread spectrum communication offers the possibility of time capture That is a packet may be distinguished and received correctly even if contending packets overlap the transmission as long as the signal strength of the contending packets is not too great Moieover if multiple receivers are available at the receiving station spread spectrum coding can be used to allow the reception of several distinct packets being transmitted with overlap on a single channel When the transmitters are widely distributed geometric or power capture is possible Roberts 1972 With or without spread spectrum if a competing Fignal is much weaker further away than the desired signal there is no interference Both types of capture can give rise to performance superior to that predicted by a simple unslotted ALOHA model On the other hand power capture gives rise to bias against the more distant transmitters because the close in transmitters overpower the ones further away Thus the probability q r of a successful transmission at a distance r from the station will decrease as r increases and the number of retransmissions increase as well as delay The purpose of this chapter is to characterize the probability of successful transmission as a function of 1 distance from the receiver r 2 the multiplicity M of receivers available at the receiving location 3 the packet arrival rate 12 1 Network Analysis Corporation 4 the time bandwidth product K extent of spectrum spreading 5 the required signal to noise ratio SN of the receivers 6 the exponent a in the inverse power law s r assumed for the transmission power of a transmitter at distance r from the receiver The situation we consider is that of a circular field of transmitters of radius R accessing a receiving station in the center with M receivers where R is the range of the receivers Arriving traffic is assumed to have a uniform rate per unit area in the field and the arrivals plus retransmissions are assumed to be Po sson distributed Particularly important for the design of a Packet Radio System is the analysis of multiple receiver stations Adding extra receivers to the Packet Radio Station adds throughput and shortens delay This is a very attractive approach because the modification is simple and is applied only at the station No modifications are required to the terminals the repeaters or their geographical location Finally the enhancement is applied directly where it is needed at the station bottleneck where all the information flow of the system must eventually pass The simulation results show that multiple receivers will in fact increase performance substantially moreover very few additional receivers are required to realize most of the advantage usually only one additional is required For addition of receivers to be effective two prerequisites must be satisfied i the traffic rate must be quite high otherwise the chance of several messages arriving simultaneously will be small and ii the spread spectrum factor K must be sufficiently large compared to the required signal to noise ratio SN otherwise even if there are sufficient receivers 12 2 Network Analysis Corporation to receive a number of simultaneous messages the interference created by the messages will cause none of them to be received correctly The q r function derived here will also be very useful in the location of repeaters to provide coverage for terminals The simplest models require that each possible terminal location be covered by some number of repeaters in order to guarantee reliable communication This type of model assumes a binary characterization of transmitter-repeater communication either communication is possible or it is nrt The q r functicn could be used to reflect the fact thaL a far away receiver does not provide as good service as a nearby one In Section 2 the model and the assumptions it is based upon are introduced In Section 3 analysis is used to predict the qualitative behavior of the q r function especially with respect to limiting values of parameters It was found for example that to a user at far distances r R the system performs as in unslotted ALOHA That is a transmission arriving at time t gets through if and only if no other transmission starts in the interval t -T t T where T is a packet transmission time On the other hand for r o for the one receiver case performance approximates slotted ALOHA in the sense that only packets preceeding t -T t t can interfere Explicit bounds on the benefits of adding multiple receivers are also given In Section 4 simulation is used to verify and extend these results Finally the simulation program is documented in an Appendix The first analysis of thr geometric effect of capture for a circular field of packet transit' cters accessing a receiver in a random access mode was Roberts 1972 Roberts made among others the following assumptions 1 the probability q of a packet being received correctly for a given transmission or retransmission is 12 3 Network Analysis Corporation a independent of distance r from the receivers b independent of whether the transmission is the first or a retransmission 2 the probability of more than one contending packet is negligible 3 noise is negligible compared to competing signal strengths Kleinrock and Lam 1972 improved on these results by relaxing assumption 1 b to allow different q's for the initial transmission and for retransmissions John Leung L—973J considered the same problem where the signal power instead of being represented as a deterministic inverse square of distance had a Rayleigh distribution to represent the effects of multipath One consequence of this is that the receiver has unlimited range Leung also essentially assumes 1 and 2 see in particular eq 7 where G r is apparently assumed proportional to r i e that „ne rate of arrivals plus retransmissions per unit area is independent of r Fralick 1972 also does an analysis of the field of terminals situation extending Roberts' results for the use of spread slotted spectrum including propagation delays He assumes 1 2 and 3 Abramson 1973 considers a central receiver in an infinite field of transmitters and determines the Sisyphus distance R which is the radius beyond which tbo expected number of retransmissions is infinite He assumes 2 and 3 Thus the critical distance R s is defined by competing signals while the R we use is defined by noise considerations All the above models assumed one receiver M l The model for spread spectrum reception is similar to those described in Kaiser 1973 p 2 McGuire 1973 and Fralick 1973a Fralick 1973a considers several models of spread spectrum 12 4 Network Analysis Corporation random access the one closest to ours is the one using Synch Preamble In particular our lower bound for q o is based on his analysis of this case Also Fraiick pointed out an error in normalization in Section 2 that appeared in an earlier version of this note For simplicity we assume that the surface wave devices for encoding the spread spectrum code are programable and that the chip code varies from bit to bit in a pseudo-random manner so that competing signals appear more nearly like noise this for example avoids many of the difficulties pointed out by Fraiick 1973 Programmable surface wave devices are discussed in Staples ana Claiborne 1973 and LaRosa 1973 12 5 Network Analysis Corporation 2 MODEL AND ASSUMPTIONS A central receiving station is receiving messages from an infinite number of terminals within a radius R where R is defined to be the range of the station that is the distance at which a terminal can just be heard The terminals send packets according to a Poisson distribution with arrival rate density p packets per unit time per urtit area The principal objective is to determine the grade of service for terminals as a function of distance from the station The grade of service q r is defined to be the probability that a message sent by a terminal at radius r from the station will be received by the station on any one transmission first and subsequent retransmissions are assumed to have the same probability of success Kleinrock Lam 1972 Having q r we can also define G r S r q r to be the arrival plus retransmission rate density at radius r where S r is the arrival rate density at raaius r oiven by 2irrp For our purposes the receiving station can be in o e of M l states o receivers busy 1 receiver busy h receivers busy We will denote these states as S S S In state S i M i receivers are busy and one of M-i remaining is awaiting a synchronization code from Ihe beginning of some packet If the receiver achieves synchronization with a new packet the receiver is captured S -► S l and is now busy in a receiving state and remains in that state for one packet transmission time T The new packet is correctly -eceived if the total power of contending signals does not become too high during the transmission time The receiver is busy for the full time T in either care When all the receivers are busy state SM all arriving packets are lost until one of the receivers becomes free We specifically ignore the possibility of false alarms that is the receiver going from free to busy on the basis of noise Thus a packet arriving at time t is assvmed to be received correctly by the station if the 12 6 Network AitalyJs Corporation following three conditions are satisfied 1 a receiver is free at t 2 the signal strength is sufficiently Wronger than ambient noise and other signals arriving in T-t t so that the receiver achieves synchronization 3 signals S' -iving in t t T are not strong enough to drow it the signal after synchronization is achieved In our model of the receiver we assume that a signal can be heard if the desired signal energy is sufficiently greater than the competing energy which consists of two elements ambient noise and the other undesired signals We are allowed to use spectrum spreading to increase discrimination between signal and the competing energy To be more specific assume we divide each bit into a coded sequence of K chips Further suppose the receiver works by integrating the received signal correlated with the chip code If the integral of the signal amplitude over one chip time is A then if there is correlation with the chip code the received energy in one bit is K A s ra for a signal at distance r If the signal is uncorrelated with the chip code the received signal is the integral of a sum of K binomially distributed signals of amplitude A which for K reasonably large approaches a Gaussian distribution with mean o and variance KA 2 s Kr a Thus received signals in synchronization with the receiver deliver after correlation a factor of K more power than competing signals of the same strength which are uncorrelated with the receiver If we let N be the ambient noise per bit the signal to noise energy ratio is 12 7 Network Analysis Corporation S 0 —2 SN -K a — a ' KL 1 N r which we require to be no less than SN for reliable reception where ro is the radius of the desired signal which is assumed to be in synch with the receiver's chip code and r i o correspond to competing signals not in synch which effectively look like noise added to the ambiert noise N The range R is determined by s a —§R SN or 2 I o N SN The parameters we wish to study are SN a and K so by judicious choice of units we may normalize the units of power and distance so that s 1 and R 1 This results in the decision criterion 1 K cT -° SN 3 w Kr sl i 0 1 See Kaiser 1973 for a similar model 12 8 Network Analysis Corporation 3 PRELIMINARY ANALYSIS The exact analysis of the probability q r of a message getting through on any given transmission from a radius r seems most difficult however we can get quite a good qualitative idea of q r by analysis This analysis will be supplemented by simulation result in the next section Since the signal power is monotone decreasing with increasing radius and the message arrivals are independent it is clear that q r is monotone non-increasing A message being transmitted starting at time t from the critical radius R 1 will be successful if and only if there is no other transmission in the interval t-T t T since any additional signal will prevent reception But this is exactly the situation for unslotted ALOHA Thus if G is the rate of message arrivals and retransmissions for the entire circular area of R radius from the receiver q R e 2 GT 4 Unfortunately we do not yet know G Clearly from 4 and the fact that q r is monotone G G u where G u is the arrival plus retransmission rate for an unslotted ALOHA system i e G is the solution of S Gu e 2GuT 2 where S TTR p is the total arrival rate We can generalize 4 somewhat For even if r R 1 if r is sufficiently large any other transmission can prevent it from being received Thus suppose we are considering a packet from r contending with a packet arriving from r R 1 the weakest possible The message from r can be heard whenever 12 9 Network Analysis Corporation 0 SN 1 ZSN X or 1 a On the other hand if r block reception q r 2GT e- r r any other message is sufficient to Therefore we have e 2GuT 5 for r r 1 As r- -o the signal power becomes infinite so that the probability of successful transmission depends only on whether a receiver is free or not For the case where M l and with perfect time capture Fralick 1973a has shown that the probability the receiver is free is -TTG' s ince there isn't perfect time capture in our model the probability the receiver is free is greater than that So we have ° ITC' Given there are one or more transmissions in t-T t the probability the receiver is captured is greater than the probability that one specific transmission say the first in the interval captures the receiver which is in turn greater than the probability that that specific transmission is received which is S G on the average 12 10 Network Analysis Corporation Thus q o 1 - Prob of transmission in t-T t tiroes the probability receiver is captured by one of the transmissions 1 - 1 - e GT § yielding q o 1 - l-e GT § 1 G 6 If we add additional receivers we get improved performance for small r but not for r r 1 In order for additional receivers to be helpful there must be sufficient traffic to keep them busy but not so much that the interference caused by nonsynchronized messages overwhelms the desired one We first determine the maximum number of receivers which can all be correctly receiving at the same time Thi s clearly happens when all signals are at the same radius and that radius approaches zero For n receivers at radius e with e • ■ of 3 has the limit SN Thus we see that Maximum number of receivers K SN 7 For example if the spread spectrum factor K were 100 and the required signal to noise power SN were 20 then at most five receivers could be simultaneously receiving correctly This indicates that the number of repeaters which can profitably be added is small 12 11 Network Analysis Corporation Another factor affecting the utilization of multiple receivers is the amount of traffic in the system Suppose the gross traffic including retransmissions is a Poisson Process with arrival rate G per second Then the number of messages being received at a given time t is simply the messages which arrived in the interval t -T T where T is the transmission time The probability P k of k active messages is then given by the Poisson distribution k _GT P GT k GT - iJ eH k K 0 1 8 We define k Q GT k I P GT i i o For an M-receiver system a new arrival at r o will be received if less than M messages arrive in the previous T seconds although sometimes a receiver will be free even if M or more arrived in the interval thus q o Q GT M-l Similarly for K- » we have q r Q GT M-l We do not know G but we can define G to be the solution of S G Q GT M-l s — S in the case K- -°° and q o — S in general yielding the bound p ü G G 12 12 Network Analysis Corporation To get an upper bound we consider a hypothetical system with perfect capture in which messages turn themselves off if they do not capture a receiver In other words a message is received correctly if and only if there are less than M receivers which are in the process of correctly receiving a message For such a system q r Q ST M-l where we assume the packets received correctly follow a Poisson process with arrival rate S Since messages do not turn themselves off our performance is worse and for real systems we have q r Q ST M-l 9 For M l we obtain i s e ST q r 10 Since a finite K will only make the system behave still worse 9 and 10 also hold for finite K It is important to note that almost axl these results depend on the processes involved being Poisson There are three processes of interest the arrivals to the system the starting times of first transmissions and retransmissions and the starting times of successful transmissions The first and third processes have arrival rates S in equilibrium while the second process has rate G It is reasonable to assume the first process is Poisson and by being sufficiently clever with the retransmission scheme used the second proress can probably be made Poisson to an arbitrarily close approximation but there is no way the third process can be Poisson tor example the probability of M l successful receptions 12 13 Network Analysis Corporation starting in an interval of length T is zero for the third process and positive for a Poisson process The Poisson approximation has been shown to be accurate for lower traffic rates and one receiver but for the high traffic rates examined here and with multiple receivers discrepancies can be expected For example safer bounds for 9 and io respectively might be 9 q r SftJSiJfcll Q ST M and for M l 10' q r J 1 ST In the simulations of the next section only the second process in assumed Poisson Now let us summarize our knowledge In general we have i q rx q r2 for o r1 r2 l _ ■ £ satisfies e -2G u T e -2GT where n q r £for o r l G„ S Gue Gu iii iv v q r e-2GT for r£i l where r —-■ ■ 1 X q r Q ST M-l q o % where G satisfies S GQ GT M-l 12 14 1 a Network Analysis Corporation vi q o 1 G vii t if K- oo and q o 2 —-— for finite K 1 1 q o 1 - l-e'GT i Finally the maximum number of receivers which can be correctly receiving messages at the same time is less than or equal to K M 12 15 Network Analysis Corporation 4 A SIMULATION APPROACH Simulation was resorted to in order to verify the relations derived in Section III and to estimate more detailed attributes of the system in particular to estimate G which is required for several of the estimates in Section III Details of the simulation method are given in the Appendix Ir general the estimates of G were quite stable with apparent accuracies of better than 1% The functional form of q r was not as successfully simulated however the simulations were consistent with the approximations and bounds of Section III within sampling error The nominal system simulated had S 1 SN 20 K 100 M 1 and a 2 T was everywhere taken to be 1« Table 1 summarizes the systems simulated Figures 1 7 are q r curves for the first seven systems simulated Figure 8 shows the change in q r obtained by adding a second receiver Systems 2 and 10 changes for adding more than one receiver were negligible in all cases Figure 9 illustrates the dependence of G on K for fixed S while Figure 10 shows the relation between G and S for K 100 and K 1000 12 16 s g K H U W z £ HHt-lrHiHr-iHtNr rsiroinr-ICNiro o oooiinvoovorN-m rj r r cocoo t Nininr ia vooocor-io o OfHQo ■HO'ir-irM CNHOOvrorotnr in b O Q 2 w D EH 23 J U H Ei r-t Nt-ii- -ifHHrHr-trMr i Ntnm V 0 D H Q IM cococor ocowcococococoooo HHinr»o Ntn»-iiHi-iMr-iCT 'T yi 5l O inOllN01O lim3iwmo W S2 u EH z w z So a « W M filN«NNN fM N NNOINMN O 04 0 X C 3 OS w w 2 s « D 9 b w OOOOOrHOOOOOOOOO OOOrHO ooooooooo rHHiH O HHHHiHHOOO H i-l H rH X W w «5 H z o o z z H w w o OOOOOOOOOOOOOOO NfNi-irM N NrM N Nf J N NfMCNtN EH H1 H EH co n co CO CO CO H NrHrHrHrHrHrHrH N N NC0COCO w OS X S 03 uw m en S EH X 3 CO z 3 •H g0 w rH e H U W « 0 o W H y c o •H •P «3 1 HrMf»iT invor ooo OH Nco rio rH rH H rH 17 rH rH 311151 I I 193853 so an Jlr 'a Talia '5 I I i1 - 1 RV man manual HHDEHM bun - m m 4 u ll 12 20 UHSLOTTED HR for System 3 FIGURE 4 3 I I '4 12 21 I HR for System 4 FIGURE 4 Ii In Illu i hdnf 35 53 Ohwi Haw mimwma 11 j t ti trr i- JrtF-Bfi O I 0 r « ■ aj I z H ■« 0 -I■M to i CO 0 M VD • « sD O 5 b O T8° 12 23 »M M KiilÜi cl I Hui 344524 33il II l I-I-- I rrI -- 4 li iI -IInine-I4- hilt- IL- - q 1 I- I I 4 41 4- 1L4if IIITI- 4 I l-d IA 01-0- 41 J n-l Ir l I t-V I II ll 4 444 4I-I1II II T i l-lI 4- 5 I r -I- -II -44I lo I II T-l-tri I I-v nzfl-IfIf l'lil-C T'j Ell II 2 1 n-cnivar 3 5- 2 an - an 12 25 I DIR for Systems Raceivars FIGURE I I I IILI I II I I ILI -I I I I II II I Ill -I I'Iv-l' HI I I I I IIH II I- IILI I-- I - 5 I II I I IILI I - I I l IITII II 0 II I I I I lrIl I LIIIOII I 9 II m 1-1-1 51- I I - ILII- I - I I I VNH H I I-II I I II009705 a 2 I937054 a a I 101 8 $103 23 0 Buaupu Ilium Zulubu I will 00 ZUDNVUKJ 12 27 J I1 -- A x-1000 x-x-lbo 0-4 I 5 FIGURE ll 10 GVI S Network Analysis Corporation 5 APPENDIX METHOD OF SIMULATION The radius from the station R o to R l is divided into ND intervals Associated with each interval I is a ring of width 1 ND and area 2 T I ND Thus each ring is assigned a weight proportional to radius of arrivals in an array RDN so that the arrival rate in the ring is RDN I SIGMA Q I is the current estimate of the probability a transmission from the I ring is successful RDL I is defined proportional to RDN I Q I so that the estimated arrival plus retransmission rate in the I interval is RDL I GAMMA where SIGMARS and GAMMA G Initially we take GAMMA SIGMA and RDL RDN The general step is to generate NS Poisson arrivals with arrival rate GAMMA The transmissions are assign d radii according to the distribution RDL and the corresponding signal powers calculated in an array S In an array ST the instantaneous power is calculated for each time at which a transmission is initiated Finally in an array SMX the maximum power over the T seconds subsequent to each start of transmission is calculated To calculate the number of successful transmissions the transmissions are considered in order An indicator keeps track of how many receivers are busy or a given transmission the program first determines which interval from 1 to ND the transmission originates from if it is in the I for example then RBX I is bumped Then the program makes the following tests to see if the transmission is successful 1 Using the ST array the program determines if the receiver can hear the beginning of the transmission If so we go to Step 2 If not we go on to the next transmission 12 28 Network Analysis Corporation 2 Is a receiver free If one isn't go on to the next transmission if one is mark the receiver busy for the next T seconds and go on to Step 3 3 Can the entire transmission get through without being drowned out by subsequent competing transmissions This is determined using the array SMX If this test is passed the transmission is assumed successful and a counter SBX I is bumped After all the transmissions are processed and improved estimate for Q I given by Q I SBX I RBX I A l is obtained and this is repeated several times until the distribution settles down It turns out that this process was very unstable at least in the estimate for Q I The estimates for GAMMA were quite easy to obtain and reliable but there were rather wide fluctuations in the Q I between iterations or when using different seeds for the random number generator The reason is apparently because the power for originations near the origin become unboundedly large and hence have disproportionate influence while the number of such events is quite small so the resulting variance is rather large This was ameliorated to seme extent by using exponential smoothing that is replacing A l with Q I RLX Q I 1-RLX SBX I RBX I where 0 RLX 1 12 29 Network Analysis Corporation CHAPTER 13 PACKET DATA COMMUNICATIONS ON MATV AND CATV SYSTEMS A FEASIBILITY STUDY 1 INTRODUCTION In 19 0 the ARPA network was still written about in terms of goals to be reached For many years small groups of computers have been interconnected in various ways Only recently however has the interaction of computers and communications become an important topic in its own right In 1968 after considerable preliminary investigation and discussion the Advanced Research Projects Agency of the Department of Defense ARPA embarked on the implementation of a new kind of nationwide computer interconnection known as the ARPA Network This network will initially interconnect many dissimilar computers at ten ARPA-supported research centers with 50-kilobit common-carrier circuits The network may be extended to include many other locations and circuits of higher bandwidth The primary goal of the ARPA project is to permit persons and programs at one research center to access data and use interactively programs that exist and run in other computers of the network This goal may represent a major step down the path taken by computer time-sharing in the sense that the computer resources of the various research centers are thus pooled and directly accessible to the entire community of network participants F E Heart et al 1970 Now these goals have been completely achieved with even further developments largely solidified For example TIPS Terminal Interface Processors to connect terminals to the ARPANET are a reality as are VDH Very Distant Host connections In fact in 1972 the result of the ARPA network development led to the conclusive statement that its performance is superior to other existing methods« Extensions to personal hand held radio terminals are in the offing using a random access mode as begun in the University 13 1 Network Analysis Corporation of Hawaii The merits of the ALOHA packet mode have been thoroughly investigated with a conclusion packet technology is far superior to circuit technology even on the simplest radio transmission level so long as the ratio of peak bandwidth to average bandwidth is large Most likely the only feasible way to design a useful and economically attractive personal terminal is through some type of packet communication technology Otherwise one is restricted to uselessly small numbers of terminals on one channel This result may also apply to many other important developments only to be discovered as the technology of packet communication is further developed Roberts 72 Both as an adjunct to the interactive packet radio mode and as an extension of the ARPANET this report describes the use of MATV and CATV coaxial cable systems for local distribution of packet data We first explain the need for a local distribution medium such as an MATV and CATV System to augment a packet radio system in urban and suburban areas We next investigate the properties of the coaxial cable systems in order to evaluate their data handling capability To demonstrate the validity of our conclu- sions actual designs are discussed for the existing CATV system in the Metropolitan Boston area Specifications are given for all required digital equipment and finally test procedures are given The overall conclusion of the study is that MATV and CATV interactive packet systems would form an excellent local distribution medium 13 2 Network Analysis Corporation 2 THE IN-BUILDING PROBLEM In urban areas two difficulties impede the reception of radio signals in buildings 1 The attenuation of signals in passing through building walls and 2 The reception of multipath signals due to reflections off buildings In a study of the in-building reception problem C H Vandament of Collins Radio concludes signal strength environment on a city street will probably need to be 25 to 30 db higher than that previously considered if direct radiation into buildings is to be considered i e no building distribution system employing amplification This is quite unattractive since this implies either excessive transmit power and or quite close repeater spacing Vandament 1973 Both of these problems can be avoided while still retaining the main idea of using ALOHA random access multiplexing instead of operating in an over-the-air broadcast transmission mode data can be sent over the existing wideband coaxial cable facilities of master antenna MATV and cable television CATV systems Recent FCC rulings require that all new CATV systems have two way capability penetrations of 40-60% of U S homes is projected by the end of the decade Sloan 971 Moreover most of the major new office buildings will have wide-band communication channels built in For example in the New York World Trade Center there is a system of switched wideband communication channels The user can select 60KHz audio channels or 15 MHz video channels and has an individual wideband cable connection to the central switch Friedlander 1972 By 1980 the wired city will be close to reality Vandament after considering radiation telephone wires power cables and other special wiring schemes for the in-building problem comes to a similar conclusion regarding the merits of coaxial cable transmission Every building will require some analysis to determine which technique is required to deliver a useable signal to a terminal inside 13 3 Network Analysis Corporation If the building has windows and is relatively close to a system repeater no special techniques will be required At greater distances a simple repeater with directional antennas focused on specific buildings will deliver the signals to interior users by radiation Buildings which are effectively shielded must have a simple dedicated repeater to receive a signal and pipe it into the building over conductors of one type or another High grade coaxial cables solve that problem nicely but this answer would probably be prohibitively expensive for the packet radio scenario of general distribution throughout every important building in the U S Where such cables exist they do offer an attractive solution to the in-building distribution problem Vandament 1973 In the next five sections we will show the technical merits of MATV systems for solution of the in-building problem and CATV systems for local distribution in high density suburban and urban areas To do this we first describe the properties of typical modem MATV and CATV systems in Sections 3 and 4 respectively 13 4 Network Analysis Corporation 3 A TYPICAL MATV SYSTEM A master antenna television system as shown in Figure 3 1 serves a concentration of television sets such as in an apartment building hotel or motel The main purpose of the MATV system as CH 3 CH 5 CH 10 CK 13 BALUN 4-WAY HYBRID USED AS A COMBINER PREAMPLIFIER AMPLIFIER SPLITTER UP TO 100 OUTLETS Figure 3 1 Typical Hotel or Apartment Building MATV System shown in Figures 3 2 3 3 3 4 is to provide a usable signal to a large number of television sets fed by a local distribution network A number of television sets connected to the same antenna system without a sign-il amplifier would not provide any of the sets with a strong enough signal to produce good pictures An all-channel 13 5 Network Analysis Corporation j BAUM WALL OUTLETS AMPLIFIER Figure 3 2 cs LEHEH3 SPUTTER Typical Motel MATV System 7 1 - AMPLIFIER 1 I 300-OHM TWIN LEAD j t DO K r DT 3 Figure 3 3 i f i Typical Home MATV System master antenna amplifier is connected to one antenna sometimes more which provides across-the-band amplification of all television signals in the VHF band and the f-m broadcast band Some MATV systems employ more than one amplifier A separate single-channel amplifier may be used as shown in Figure 3 5 to provide greater amplification of a single channel Generally a separate antenna is used with a single-channel amplifier 13 6 Network Analysis Corporation T GARDEN APARTMENT 3-FAMIIY HCMIS ETC AMPLIFIER 300 -OHM TWIN LEAD oe s ö Figure 3 4 4 MATV System for Multiple Dwelling For reception of UHF television stations a UHF-to-VHF translator is required V V BROADBAND AMPLIFIER SINGLE CHANNfL AMPLIFIER -f LEVEL CONTROL COUPLER TO DISTRIBUTION NETWORK Figure 3 5 Use of Single Channel and Broadband Amplifiers for Receiving Distant Stations For MATV systems with more than 100 outlets further amplification may be required and in a large office building cascades of two or three amplifiers might be expected Never- 13 7 Network Analysis Corporation theless compared to CATV systems - to be described in the next section - modern MATV systems are relatively uncomplicated media for data transmission Signal to noise ratios of better than 43 db are reasonable there are few environmental problems since the system is i oors there is minimal temperature variation and amplifier cascades are low since the wide band capabilities of 0 5 inch coaxial cable are used In a CATV system the signal at the building is received from a cable distribution system rather than from antennas However the in-building part of the system is essentially unchanged from that used for an MATV system 13 8 Network Analysis Corporation 4 A TYPICAL CATV SYSTEM CATV systems are an historical outgrowth of MATV and com- munity antenna television systems CATV systems perform roughly the same function for an entire town that a MATV system performs for a building namely the distribution of TV singals to many terminals from a central reception area Although the basic engineering strategies are the same for MATV and CATV systems the CATV system is different in one crucial aspect since it is larger as many as thirty amplifiers may have to be cascaded to deliver a TV signal to the most distant terminal in the system Therefore the system design requirements are stringent very high quality amplifiers and off the air reception equipment are essential In order to motivate our proposal of data options and techniques Tor CATV systems a detailed description of these systems is in order CATV systems in the U S A are almost universally tree structured networks of coaxial cablas installed for the distribution of broadcast type television signals from a central receiving station called the head end to home type television receivers Different television signals which may be received at a central site or relayed over long distances by microwave systems are processed at the head end and frequency division multiplexed onto coaxial cable for distribution Coaxial cables now in use are universally 75 ohm inpedance types usually of seamless aluminum sheathed construction foam polyethylene dielectric and solid copper or copper clad aluminum center conductor The coaxial cables range in size from 0 75 inch outer diameter for main trunk cables through 0 5 inch size down to a 0 412 inch size for local distribution The service drop lines to the houses are usually flexible cables of about 0 25 inch diameter The useful frequency range includes the VHF television band 54-216 MHz and broadband transistorized amplifiers are installed with equalizers to compensate for cable losses Practical systems are aligned to be unity gain networks 13 9 Network Analysis Corporation with amplifiers spaced about 20 db at the highest transmitted frequency Cable losses range from about 1 db 100 at 220 MHz for the 0 75 inch size cable to about 5 db 100' for the flexible service drop cables Power division at multiple cable junctions and taps into subscribers' homes are accomplished through hybrid and directional couplers All system components are carefully matched to 75 ohms to minimize internal signal reflections within the system System amplifiers are subject to rigorous linearity specifications Amplifier overloads manifest themselves as cross-modulations between chenr ls and as undesired second and third order intermodulation and harmonic products Amplifier operating levels are bounded on the lower side by system signal to noise ratio objectives which are about 40 db over a 4 MHz band for reasonable acceptable performance as a television distribution system A typical system will have amplifier inputs at about 10 dbmv and outputs at abouc 30 dbmv System operating levels are controlled by automatic gain control circuits driven by pilot carriers and thermal compensation devices More recent cable systems have been built using a hub principal in which tree structured networks originate from a number of hubs throughout the community serviced see Figure 4 1 The hubs may contain equipment for more elaborate control of signal levels and it may be possible to perform some special switching functions such as the interconnection of sub-trunks for special purposes hub Figure 4 1 Hub System 13 10 Network Analysis Corpora dan Two-Way CATV Configurations FCC regulations now require that new CATV systems must have two-way capability Practically speaking this does not mean that all new systems are two-way systems but rather that amplifier units are installed with forward amplifier modules in place and with distances between amplifiers constrained so that at some future date reverse amplifier modules can be installed for two-way operation However a number of actual fully two-way systems are presently being built and the number is increasing rapidly Most present two-way systems use the configuration in Figure 4 2 Filters at each end of the station separate low L and high H frequencies and direct them to amplifiers usually referred to as downstream from the head end and upstream toward the head end A number of possible two-way configurations are shown in Figures 4 2 4 3 and 4 4 Jerrold 19713 The final choice between single cable two-way multi-cable two-way and multi-cable without two-way filters will probably be made on the basis of marketing opportunities for special services There are no government regulations s to minimum specifications for a system Hence we will base cur discussion on the characteristics of a representative two-way system the Boston complex This system is being built in about 10 stages one of which is already installed and the final phase of which is to be completed within a year At its completion Boston will be one of the largest systems in existence in the U S The Boston system uses the feederbacker configuration shown in Figure 4 4 with the frequencies assigned to the upstream and downstream paths specifically indicated Data transmission on CATV systems will generally have to be fitted into space not being used to TV channels or for pilot frequencies Hence it is best to first describe the frequency allocation for video signals TV channels are allocated six Megahertz 13 11 Network Analysis Corporation FIGURE 4 2 W— TNUW Mwurim DNKCrKMU COun CI I ranug I«U«I our nfrumi T umml fCCOC MANCH ajiUM TKUM unino ■»ecTioML count FIGURE 4 3 Two-way CATV Repeater with feeders ' Pomu o « « 'ic» omccnoxtL counj r f JVTHUII« VTKUWXI I'TIIUW FIGURE 4 4 _ 5-108 5-108 ■f Tuim mux« »nine 54-260 5-30 «ccriouL count Dual Trunk Single Feeder Station Boston Configuration 3 12 Network Analysis Corporation bandwiths Broadcasted TV channels are in the Lo-VHF range 54 MHz-88MHz the Hi-VHt range 174 MHz-216 MHz and the UHF range 470 MHZ-890MHZ T P TV frequency allocations on able are different They partition the 54-3C0 MHzspectrum ao follcws 5-5 KHz Sub-VHF 54-88 MHz Lo-VHF Mid-band 88-174 MHz Hi-VHF 174-216 MHz Super-band 216-300 MHz There is still discussion going on as to whether the mid-band should be used within a cable system because of danger of interference to aircraft navigation in case of signal leakage out of the cable Data might be squeezed into bands not used by TV signals Some space is available below Channel 2 at 48-54 MHz The space between Channel 4 and Channel 5 72-76 Mhz might be used for low level data signals High signal levels in this area could cause harmful picture interference on some TV sets A more likely situation is that two 6 MHz video channels - one upstream and cne downstream - would be set aside for data transmission The simple fact is that 2 to 30 channels are available on a single cable system and 42 to 60 channels on a dual cable system These channels have not all yet been pre-empted by ■ ■'■' CQO transmission 13 13 ■•■•--- Network Analysis Corporation 5 DATA OFTIONS ON MATV AND CATV SYSTEMS Based on the details of MATV and CATV systems we can demonstrate the merits of in-building and local distribution on MATV and CATV systems and describe detailed data options for experimentation and practical implementation Most two-way systems are being developed with an upstream channel designed to permit input from virtually any location in the network The result is a large number of noise sources being fed upstream toward a common source Individual cable television amplifiers usually have a noise figure of about lOdb for a 6 MHz channel Cascading amplifiers can increase effective system noise figure by 30db or more Nevertheless we shall see that system specifications on signal-to-noise ratio for CATtf systems are stringent enough so that packets can be sent with existing analog repeaters and no digital repeaters such that bit rate error probabilities are negligible For example in Bosto i the worst signal-to-thermal noise ratio is limited to 4 3db and the worst cross-modulation to signal ratio is limited to -47db System operators may want to limit data channel carriers to a levcd of 10 to 20db below TV operating levels in order to minimise additional loading due to the data channel carriers Switzer 1972 The cable operator at least for the time being s making his living by providing a maximum number of downstream television channels and will accept data channels only on a non-interfering basis Accepting these restrictions in the worst case we would be limited to 2 3db signal to thermal noise ratio and -27db crossmodulation to signal ratio Let us consider both of these sets or restrictions to determine the resulting CATV system performance for random access packet transmission From the calculations in Appendix A we ha e the error rates shown in Table 5 1 The calculations are performed for a FSK system with incoherent detection to determine a lower bound for system performance 13 14 nf V iiMIM ih-tir -- w - - TiM iMi Network Anatyiis Corporation TABLE 5 ERROR RATES FOR FSK System Label Type of Specification 1 Nc S S N m Pe A Boston Specs -47db 43db 2 V2e-5'148 1 2X10-2'239 B Boston Specs -47db 43db 4 3 4 e C Boston Specs -47db 43 db 8 7 8 e D Boston Specs - degraded by 20db -27db 23db 2 1 2 e 51 x 5 x 10 22 1 -57 1 _-MQ sa 3 4 x 10 24b -11UfH -45 7 8x10 It is well known that for effecti signal-to-noise ratios above 20db there is a threshold effect for error probabilities This is born out by the negligible error rates in Table 5 1 Even for the degraded specifications the error rate is low enough for the most stringent practical data requirements At a rate of 10 pulses second the FSK signal will occupy the 6MHz bandwidth Switzer 1972 with negligible intermodulation into TV channels Schwartz et al 1966 In Figure 5 1 we plot the maximum number of active terminals for the systems in Table 5 1 as calculated in Appendix B The civrves labeled A B C and D correspond to the slotted systems in Table 5 1 labe1 B C and D The lines labeled A' B' C and D' are for t sponding unslotted systems We can now - „xiie Figure 5 1 to determine system performance under some typical data transmission requirements For a data rate of 40 bits second per terminals a single trunk can handle 900 terminals with a slotted ALOHA system 1 Megabit sec with an error rate of 10 -22 at a signal to noise ratio degraded by 20db The average number of TV sets per trunk in Boston is approximately 27 000 Hence the simplest modulation scheme will handle cms third of all terminals in Boston as active terminals At lOOKbits second the system will handle 900 active terminals 13 15 JkMMIiliUHM mmmm IM H M M ___ Network Analysis Corporation USL r roia iS5no5T SYSTEM ' x 10 pu ses Bec FIGURE 5T1L NUMBER OF TERMINAL PER TRUNK VS BITS SEC PER TERMINAL 13 16 I Network Analysis Corporation i We will also consider the introduction of a number of basic data processing options into the CATV system in order to make our data transmission system adaptable to a variety of traffic requirements while satisfying the system constraints We will use the terminology of the cable TV industry in describing the direciton of signal flow Signals traveling from the head end toward terminals will be said to be directed in the forward direction on a forward link and signals traveling from terminals toward the head end will be said to be directed in a reverse direction on a reverse link A convenient synonym f r forward will be downstream and for reverse will be upstream To install the device to be described in the forward and reverse channels simple diplex and triplex filters can be used More detailed specifications for the filters and the data devices are giver in Appendix E CARRIER FREQUENCY CONVERSION In the simplest version of a data system two carrier frequencies are used one for forward transmission from the head end to the terminals and one for reverse transmission from the terminals to head end Let us call these angular frequencies m and w respectively The next simplest option is to use frequency converters at a small selected set of points in the system In the forward direction the converter converts from OJ to w_ and in the reverse direction it converts from w _ f f_ r to a ' The net result is that the terminals still receive and transmit r at the frequencies w- and co However in the trunk between the converters and the head end there are four frequencies in use u j' r r CJ and CJ' so that in these trunks twice the traffic can be handled The converter and the other devices to be described in this section are shown schematically in Figure 5 2 The advantages of this scheme are a All terminals are identical b The converters also act as digital repeaters to reshape signals c The capacity of the system is increased since two channels are available in each direction 13 17 a - - v «fa i » ■■-■ ■ -iitirt'-fllttfei«MMrT--'lini --» -»- - '- -- ■ Network Analysis Corporation u 'f dL a converter u'f dH b compressor d forward router e local router Figure 5 2 Device schematics devices indicated by squares Carrier frequencies u r# w'r f reverse Uf w'f forward High data rate d • Low data rate d 13 18 Network Analysis Corporation ROUTING In the interactive packet system there is no requirement for routing since the basic premise is that all receivers listen to all messages that reach them and merely select the ones addressed to them Nevertheless we will consider the addition of some primitive low cost routing schemes to study their effect on system capacity In the central transmission mode there is routing needed in the reverse direction since all messages reach the head end along the unique paths from the originating terminal In the forward direction the signals at frequency u' are blocked by filters at the converters and yields a simple form of routing In fact at any section of trunk not requiring signals at cj' filters ca- be idded to block w' Adding these filters does not increase system capacity but may be useful if the frequency w' can be used for local signaling when not being used for data transmission At any junction containing a converter digital routers must be added to send messagas at u f down the trunk to which they are addressed rather than all trunks Such a router may be added at any other point in the system as well This is called forward routing and can increase system capacity Forward routing requires a digital router which can read and interpret message addresses Let us now consider these system options in the presence of local traffic The option of frequency conversion is unaffected and performs in exactly the same manner as in the central transmission mode However an extra routing option is available for local transmission In particular if two terminals are on the same trunk then the message between them can be intercepted and routed at a routing station rather than travel all the way to the head end Such routing is called local routing Local routing reduces the traffic on the main trunk 13 19 Network Analysis Corporation COMPRESSION As the next more complicated option the data rate as well as the carrier frequency is changed at a converter i e a compressor can be used The advantages of this arrangement are A All terminals operate at low data rate B On heavily used lined near the head end a higher data rate say one megabit second can be used to increase the number of potential active users or decrease the delay C Even though a section of the trunk can carry high data rate traffic at carrier frequencies to' anand another users can still use the system at the low data rates at co and cof Thus the number of compressors required is small D At the low data rate signal distortion is kept to a minimum CONCENTRATION Finally the compressor at junctions may be replaced by a concentrator That is messages arriving simultaneously on two or more links in the reverse direciton are buffered and sent out sequentially at the higher data rate This essentially makes the system downstream from the concentrator appear to operate at the higher data rate and hence increases the system capacity even further With the use of converters compressors concentrators and routers we have a highly flexible interactive packet data system which obviously meets most of the system requirements of capatibility with the CATV system the packet radio system and the population In particular the system has the following characteristics A The number of active users that may have access to the system can be readily controlled by varying the number of converters compressors concentrators and routers B The transmission rates at every terminal are at the low data rate of 100 kilobits second C Terminal equipment is inexpensive because modulation takes place at the low data rate D All terminals receive and transmit at the same frequencies and data rates 13 20 Network Analysis Corporation FREQUENCY DIVISION MULTIPLEXING In case the data rate is limited by the head end mini-computer an available option is to frequency division multiplex several 100Kbits sec channels each of which is processed by a separate head end mini-computer The assignment of these options in an optimal fashion requires detailed expressions for the traffic in the links Formulae for the traffic are given in Appendix C and are used to give an augmented design for the Boston system in Appendix D 13 21 ii Network Analysis Corporation 6 FUNCTION OF EXPERIMENTAL DIGITAL SYSTEM DESIGN The previous considerations indicate the desirability of developing a system of MATV and or CATV lines for inter- and intrabuilding communication to and from packet data terminals A picture of the system is shown in Figure 6 1 In order to communicate through the cable system each terminal will be connected to an interface and modem A minicomputer will be connected to the cable system at its head end by means of a similar modem and modem-to-computer interface The minicomputer is used as a test device to A Receive and generate basic traffic to establish the viability of the system configuration B Provide message loading to determine limits of system performance C Demonstrate the functional capabilities required for the head end processor D Determine the performance required to communicate with external facilities 13 22 ■ •- Network Analysis Corporation I TERMINAL TO TV INTERFACE CABLE MODEM MATV or CABLE CABLE MODEM ATV SYSTEM COMPUTER TO TV INTERFACE 4 SPECIAL INTERFACE TO EXTERNAL FACILITIES 1 FIGURE 6 1 SYSTEM DIAGRAM 13 23 •- -■ mum - ■■- - r- ■- --- ■ ■' ■ - TEST MINICOMPUTER HEAD END Network Analysis Corporation 7 SYSTEM CONSTRAINTS In specifying hardware a dominant consideration ic the fact that the interactive pcket cable transmission system must interface with a CATV system and a packet radio transmission system among others and an existing population of unsophisticated users Thus any hardware innovation must satisfy the following three classes of system constraints Interface With CATV System Two Way Options The data transmission system must be readily adaptable to a wide variety of existing CATV system designs and two-way options Data Rates The data signals must not cause visible interference with video signals Installation If auxiliary data equipment is to be added to the CATV system it must satisfy the following requirements • It can be installed with only minor changes in the CATV system • It need be installed in only a small number of locations • It can be installed rapidly in early hours of the morning to prevent interference with TV service Low Cost To maximize the marginal utility of data distribution over the CATV system any equipment introduced must be inexpensive Depending upon the data rates and bandwidths involved the radio and CATV systems can be arranged to share sone modules at the baseband or IF frequency range 13 24 -1— --■ - -- ■■ ' - - - ■ • ■ ■■■■■■ ■■ Network Analysis Corporation Interface With Population Population Density Variations Standard transmission configuration options must be available for systems of various sizes population densities and percent of active users Because of the huge number of potential users all terminal equipment must be simple and inexpensive Unsophisticated Users To minimize user interaction with the system operating mode all terminal equipment must be the same for each location it must use the same frequencies and data rates and it must have no options for equipment modification by the user ÜMfirrtÜiTiWi' rriifMirr ■ ■---■ -—■— 13 25 Network Analysis Corporation 8 COMPONENTS OF EXPERIMENTAL SYSTEM With the overall system plan described in Section 6 and the specifications described in Section 7 we can now develop a detailed description of each system coi ponent These components are examined in depth since the system under consideration must be compatible with both CA7 V and data transmission technologies Systems similar to the one proposed have never been designed or built Hence major system components must be designed to esta- blish the difficulty of meeting technical requirements and to ultimately establish a cost for each component A future report will study in detail the cost performance tradeoffs of this system versus other local transmission methods involving other technologies such as packet radio p j-led multidrop lines dial up and other communication techniques 13 26 Network Analysis Corporation 8 1 MATV AND CATV SVSVEMS The digital MATV and CATV study should be carried out in two phases Phase one will develop data transmission techniques for a locally built MATV system In the second phase this tech- nology will be transferred to an existing CATV system The advantages cf this mode of operation are the following • The MATV system will be local and hence there would be no initial problems of equipment transportation • There are no initial restrictions on TV interference or picture quality • There are no initial restrictions on carrier frequency or bandwidth • The initial system can be varied in structure and performance to approximate the degradation in any CATV system • A final advantage of performing the tests on high quality well built MATV system is that it would completely prove out the viability of using MATV systems to solve the in-building distribution problem Although MATV equipment is generally poorer quality than CATV systems there should be only minor technical problems with the local MATV system since cascades are low and environmental conditions are good The local system will also provide a standard to which older poorly built MATV systems must be raised for data transmission capabilities The MATV system should meet the following specifications f • The system will have a separate antenna and pre-amplifier for each channel so the levels for each channel can be controlled independently 13 27 ÜÜMÜMü ■miiiii-im»rtfMWr- II i ■ ■■ «Mimiw w Network Analysis Corporation • All available off-the-air channels will be received • The system will cover the full VHF and UHF range • The head end amplifiers will be driven at full output capability of about 55 dbmV in order to test significant noise and cross modulation figures • The system will be two-way so that at any tap a signal modulated by digital data can be inserted and received at any other tap This will be done by feeding the signal bacV to the head end and redistributing it through an amplifier after conversion • The system will contain at least one extender amplifier on a leg of at least 1500 feet to simulate paths in a large building • The system will contain converters so that signals can be converted from a sub-VHF channel to a mid band channel A block diagram for the system is shown in Figure 8 1 1 and a bill of materials using Jerrold equipment is given in Table 8 1 1 Once the equipment and techniques are perfected for the MATV data system they must be tested and modified under environmental operating conditions on an actual CATV system CATV systems use much higher quality equipment than do MATV systems but have much longer cascades Since the test CATV system should be an operating system there will be certain restrictions on test operations The requirements on the data transmission are as follows • The data signal bandwidth be limited to an available 6 MHZ TV channel The placement of the signal is still being investigated If operation were to be at %70 MHZ the 4 MHZ guard band between 70 and 74 MHZ could be used 13 28 m Network Analysis Corporation The data signal must not yield visible interference with TV service A reasonable guarantee is achieved if the data signal is kept 20 db below the video transmission 13 29 - l— -a -M mj„ m may 10 HWDVIG H3019 I I EHDSIJ 2 15' my 4 21- a hurl-I lu- Int-4 mm lam-mn- mm a um- mm- m Network Analysis Corporation Network Analysis Corporation MATV SYSTEM BILL OF MATERIALS QUANTITY 4 5 5 9 5 2 10 5 3 2 1 2 2 1 1 1 1 38 1 1 1 4000 ft DESCRIPTION JERROLD CATALOG NUMBER J-Series J-Series J-275 TPR TPR 1 43 3963 PPS-8A THPM UCA TLB-2 THB-2 SCON-Sub-V 1597 1592B LHS-76 FCO-320 C047 1596A UT-82 SPS-30 60A — SLE-300-2W JA-500-cc-J Lo band VHF antenna Hi band VHF antenna UHF antenna VHF preamplifiers UHF preamplifier preamplifier power supply VHF amplifier UiUT amplifier trap filter trap filter subchannel to VHF converter four-way splitter UHF VKF two-way splitter VHF VHF multiplexer UHF VHF multiplexer subchannel - VHF multiplexer two-way splitter VHF UHF Subscriber taps power supply rack and miscellaneous hardware CATV exterder amplifier 5 inch coaxial cable TABLE 8 1 1 13 31 mm ■■ _ _ - ' ' ' -- ■ Network Analysis Corporation 8 2 TERMINAL INTERFACE A The interface can use a non-slotted ALOHA random access mode The first transmission as well as subsequent retransmissions will be randomized over time B The interface will transmit and receive data to a suitable modem at a rate of 100K or IM bits per second Data will be supplied to and received from the modem in bit serial form The interface will be able to provide crystal controlled clock signals to the modem or utilize moaem provided clock signals along with modem data C The interface will provide and receive data for the interactive terminal at the rate required by the particular terminal The jxact rate chosen will be selected from the rates given below by means of simple plug changes or terminal block jumper wiring at the interface unit The data rates possible are 110 134 5 150 300 600 1200 2400 bits bits bits bits bits bits bits per per per per per per per second second second second second second second The terminal input and output rates shall be independently selectable In addition it should be possible to control the transfer of data to and from the terminal by means of an externally supplied clock signal s which is below 2400 bits per second D The interface shall be capable of mitting 5 6 7 and 8 bit characters The character shall be selectable independently receiver by means of plugs or jumper straps receiving or transnumber of bits per for transmitter and within the interface 13 32 inn ■tl -L- —_L ■ ■■-■■ ■■' ■ ■■ ' ■ - ■ ■ ■ ■■ ■-■- - ■■ _ Network Analysis Corporation E The interface shall be capable of transparently receiving or transmitting all bits included in each character including a parity bit independent_y for transmitter and receiver F system The following formats will be used for the TV Terminal 1 Data Packets HEADER 2 TEXT CHECKSUM Acknowledge Packets HEADER CHECKSUM The format within the header will be as follows DEST I D 4 0 bits SOURCE I D CONTROL CODES MESSAGE NUMBER TERMINAL RCVR RATE 8 bits 4 bits 4 bits 40 bits The field sizes are chosen to allow expansion to a reasonable number of terminal interfaces on a given TV system and to provide sufficient control codes for system operation There are three possible means of identifying source and destination in the TV Terminal Interface A Log in to the interface via the terminal and establish the ID codes which the interface then uses in each header B Use short hard wired or switch selectable interface ID codes for header information The user of the terminal logs in to the head end to identify fully C Use full switch selectable ID codes on the interface into which the user sets his ID number A likely choice is a Social Security number of 9 4-bit digits No further identification of the user is required to the head end The first alternative is unattractive because the implementation of a dialogue capability between the terminal and the interface will be more costly and complicated than is warranted A hardware design which allows C also allows B as an alternate later on with only 13 33 MMI « ■'' --■ Network Analysis Corporation software changes while the reverse is not true For this reason the initial test interfaces will be built to allow insertion of a 36 bit 9 4-bit digits ID code for source and destination If at a later date it is desired to use a log in procedure at the head end the switches will be used to set in a smaller interface ID code Since there are boundaries at 8 and 16 bits due tc most mini- computers which might be used at the head end of the CAT MATV pystems initial choice of 40 bit fields for both source and destination ID's is recommended An 8 bit control code field should also be adequate The control code field will contain information such as message ID and acknowledge bits The total header length is then 96 hits or six 16 bit words G The following description of the proposed operation of the transmitter section of the TV Terminal interface assumes that the terminal has not been operated with the interface prior to this operation 1 The switches jumpers and plugs on jr in the interface should be set to conform to the parameters of the terminals This includes input and output data rates character size and interfacing conventions such as EIA current loop etc 2 The initial parameters which are required for operation with a given head end computer are set in via switches plugs or jumpers These parameters include source and destination I D codes and special escape characters which upon receipt by the interface cause initiation of various functions if any As an example the character sequence which when received from the terminal causes the interface to initiate message transmission is one such parameter 3 The terminal should be connected to the interface and modem and A C power should be applied to all units 13 34 n mM» l rim man MI -wiiiViW - jkiji L -'i '-i läSiäBäfe -JfcAfc ' Network Analysis Corporation 4 The terminal operator should compose the first message and enter it on the terminal keyboard The interface will accept and buffer the message up to a maximum number of characters For interactive terminals the maximum number of characters will be 125 the maximum line length Depending on the terminal type and mode of operation the interface night provide data character echoing to indicate correct message receipt to the terminal operator 5 Upon receipt of the escape character sequence from the terminal line terminator such as carriage return line feed or a similar sequence or upon filling of the interface buffer a transmission would be initiated from the interface and the message would be transmitted at 100K or IM bits per second Upon transmission of the message a timer would be started to time out the reception of an acknowledgement from the message destination The timer will serve two functions a time out the reception of an acknowledgement of the transmitted message from the head end for retransmission by the terminal interface and b randomize the starting time for the retransmission The fixed minimum delay before acknowledgement should be slightly greater than 14 milliseconds The exact number will be chosen later and will reflect the ease of generation of the hardware and be based on a multiple of an available clock rate The random interval of delay with respect to the starting time for the retransmission will vary from 0 to 5 full packet intervals 0 to 64 milliseconds with an exact choice determined in the same manner as for the fixed interval The maximum random interval will be divided into 1 2 millisecond sub-intervals as the various transmission starting times corresponding to 128 possible starting delays If the timer runs out 13 35 MMj--»j» ftai -■■- i r-inttmtf nnitfiiiftfciiii ■ ■ c - £-- - i«iM Jü Network Analysis Corporation without the reception ot an acknowledgement the message is retransmitted The transmitter retransmits a message N times where N is selected between 0 and 15 by means of jumpers or a switch in the interface If after N retransmissions no acknowledgement has been received an indicator will be activated to notify the terminal operator of failure to communicate with the head end computer There will be a Packet Acknowledged light on the interface which allows the terminal operator to know if the packet he last sent has been acknowledged and tells him when he can start to send the next packet In the case of an unacknowledged packet the interface will refuse any new data from the terminal and that state may be cleared by pressing a reset button on the interface 6 As soon as an acknowledgement is received the local copy of the transmitted message may be released and a new message accepted from the terminal for transmission With this type of operation only one message may be handed at a given time by the interface Once a given message has been accepted for transmission by an interface the terminal user must wait until either the message is sent and acknowledged or the message is cleared by the interface reset button 7 A preliminary flow chart for operation of the transmitter is shown in Figure 8 2 1 H The description of the proposed operation of the receiver section of the TV Terminal interface assumes that the terminal has not been operated with the interface prior to this operation 1 The parameters of the terminal should be set into the interface as in steps Gl G2 and G3 above 13 36 i i-iiii-ii'iattiriilMr ii Network Analysis Corporation 2 Upon detection of modulation on the TV channel the raw digital data will be passed through the receiver and bit and character synchronization will be obtained 3 The header will be inspected to see for which terminal the message is destined If the message is not for this terminal it will be ignored 4 If the message is destined for this terminal the checksum will be checked to insure that the message is error free be ignored If there are errors the message will 5 If the checksum is valid the header will be inspected to see if the message indicates an acknowledgement or other control function If so appropriate action will be taken For example if the message is an acknowledgement the transmitter will be notified to drop the copy of the last message sent and will be able to accept a new message 6 The message text will be received and stored in a buffer in the interface and if an acknowledgement is required the interface will transmit one to the message 13 37 M Ufite —- _ Network Analysis Corporation TV TERMINAL INTERFACE TRANSMITTER FLOW CHART 1a INITIALIZE 1 V V KMfiK UW 1 ANO INPUT MESSAGE READY • i yss i V TRANSMIT PACKET UNLOCK KEYBOARD 1 START ACK TIMER 1 I NU YES ACK RCVD L P«s NO ACK TIMER RUN OUT YES 11 TEST NUMBER OF RETRANS AGAINST N A RESET PRESSED NO MATCH MATCH SET ALARM INDICATOR FIGURE 8 2 1 13 38 ÜÜBH — itL - _ Network Analysis Corporation source The interface will sense when the terminal is turned off using the Data Terminal Ready DTR signal and will reject all packets received for that terminal during terminal power off conditions The head end will not send messages to the same terminal interface without waiting a fixed safety period The duration of this safety period will be determined at the head end by the specific terminal receiver data rate information which is a part of the header of all packets v hich originate from that terminal interface The acknowledgement from the terminal interface will be sent to the head end simultaneously with the sending of the message from the interface to the terminal 7 The number of the most vecently received message will be stored in the interface logic to allow detection of duplicate messages 8 A preliminary flow chart of the operation of the receiver is shown in Figure 8 2 2 I A Cyclic Redundant Code CRC checksum will be employed on the data for error control in the TV Terminal system The checksum for the message text will be chosen to provide adequate undetected error probability under channel conditions which are expected to be encountered in the TV system The analysis and experience of the Packet Radio and ALOHA systems will be used to pick the best checksum Bcr hardware estimates assume thi the ARPANET type of 24 bit CRC will be used in the TV Terminal interface 13 39 ■■-- -- - «MM HlHMTli Network Analysis Corporation TV TERMINAL INTERFACE RECEIVER 7JJCM CHART f NO 1 PACKET RCVD YES NO FOR THIS TERMINAL YES NO HEADER CHECKSUM OK YES YES HEADER ACTION INDICATED SET FLAGS zi— W NO DTR AND MESSAGE TEXT CHECKSUM OK YES OUTPUT DATA DO FLAGS SEND ACK TO TRANSMITTER J FIGURE 8 2 2 13 40 - ■ - Nefivork Analysis Corporation EJ strical Specifications A The interface shall be capable of being configured to match u wide variety of terminal requirements This flexibility shall be provided either by having a set of the various possible circuits required in each interface and selecting the proper form by jumpers of plugs by having a set of sub-modules which can be interchanged in a given interface to adoj L to a particular terminal's requirements or ideally but possibly quite difficult by having a single universal type of interface circuit which can be easily adapted to each terminal requirement The types of requirements which can be expected are 1 2 4 TTY Current loop @ 20ma or 6 0ma EIA-RS-232 Either full or partial depending on the terminal CCITT Either full or part-ial depending on the terminal MIL STD 188B 5 Standard low level Signaling Interface 6 Specials 3 In all cases the interface circuits should prevent or minimize damage to either the interface or to the terminal under conditions of short circuit open circuit or voltage or current transients State-of-the-art isolation techniques will be used including optically-coupled interface circuits and protective diodes on sensitive elements B The interface will be designed to match the choice of modem The same isolation and protective features used in the connection of the interface to the terminal will be included in the circuits which connect the interface to the modem C The power supply and interface circuits will be housed together Input power requirements are 1 2 110 volts A C 60 Hz single phase 3 Estimated input power required less than 100 watts 13 41 Network Analysis Corporation The power supplies will provide suitable voltages and currents for the operation of all circuits and modules within the interface Standard modular off-the-shelf supplies will be used whenever possible The interface will have a master power switch power-on indicator adequate protective fusing transmission and reception status indicators and a reset button D The logical design of the interface will be realized using standard integrated circuits and components The possible use of Large Scale Integration LSI logic modules such as a microcomputers and Read Only Memory ROM will be investigated The characteristics of available microcomputers will be carefully studied and a choice wil1 be made based on the TV Terminal interface requirements At a later date for reasons of improved microcomputer components or desired compatibility with other packet systems a different microcomputer can be selected and programmed to perform the same functions without major hardware changes The project will result in a reliable cost effective interface with sufficient flexibility to allow reasonable system modifications during testing 13 42 j Äto ■■----•- Network Analysis Corporation Mechanical Specifications A The interface will be packaged in an enclosure which is capable of standing alone The estimated size of the interface is approximately 19 wide 20 deep and 5 high The interface will have a 6 power cord and suitable connectors or terminal strips to match the connections to the terminals and modem with which the interface will operate Sound construction practice will be used throughout with an emphasis on ease of assembly and maintenance along with low cost The estimated weight of the interface is less than 30 pounds B The front panel of the TV Terminal interface will have a power switch and whatever other switches and visual indicators are required for operator assurance such as power-on and incomplete transmission All ether switches connectors and seldom used controls will be mounted in a conveniently accessible yet protected fashion Some connectors will be mounted on the rear panel of the interface while other controls and terminals will be accessible only with a set of tools such as a screwdriver or key to open a service access panel or to remove the protective cover s 13 43 CM» ■ _•__ - Network Analysis Corporation BLOCK DIAGRAM OF TERMINAL INTERFACE FIGURE 8 2 3 The cable modem data and control signals pass through appropriate level-conversion logic on entering the terminal interface Modem control signals and status signals are set or sensed by the micro computer program via paths in the micro computer I O multiplexer and controller All incoming data are passed through a data examination register where special high speed character detection logic looks for synchronization characters and enables the checksum verification logic upon synchronization All synchronized data are stored automatically in a high speed received packet buffer First In First Out - FIFO Upon completion of reception of a packet the micro computer is interrupted and begins to process the packet The checksum is verified and if false the buffer is cleared and the sync logic is reinitialized If the checksum is verified as true the packet header is examined for destination and if no match is detected the receiver section is reinitialized and the buffer is cleared If a destination match is detected the appropriate acknowledge and control information is stored in The Random Access Memor RAM and the data is enabled to pass on a byte basis to the Uni- i -i- l Asynchronous Receiver - Transmitter UAR-T which converts the parallel data bytes to serial asynchronous data at the terminal speed The data passes through appropriate terminal level conversion circuits before leaving the interface The terminal control and status sense circuits are also connected to the micro computer and the I O multiplexer The micro computer can insert or delete characters in the actual data stream between the received packet buffer and the UAR-T as for example in the case of an acknowledge for a previously transmitted message where no data would be passed to the terminal Data from the terminal is automatically stripped of start-stop bits by another UAR-T and stored in byte format in the transmit packet 13 44 ■ •MuaaiuuB Network Analysis Corporation buffer Upon detection of the terminal special end-of-line character or on filling up a packet the micro computer is interrupted and attaches the header information to the data in the transmit packet buffer» At the appropriate randomized time the data is gated to the output register and the checksum generation logic is enabled The information about the message for retransmission purposes is stored in RAM and the message is recirculated in the transmit buffer at the same time it is sent to the modem The micro computer controls the number and timing of retransmissions based on acknowledge information from received packets The crystal clock provides timing pulses to all circuits as required 13 45 'iliitMfliilttiitiiififr -1a üüMii t ii« - « DATA EXAM SYNC I IOUIC IN LE RT 1 L5 PACK ET I mu l_'f IVCIWOIR 'r-a 9 runvrw- stun n Iu 4 I 1' 1 SENSES HENHRS unlt' 9 9Mw CIJFCK but Wart - CEIFCKFUH our n q Tl l'llr'l 1 l lh hH InnFlaura- 5-1- 3 BLOCK DIAGRAH muhh' Network Analysis Corporation 8 3 MODEMS For initial experiments a 2-phase differential phase shift keyed DPSK coherently detected signal with a 100 kilobit data rate is adequate This selection of parameters enables the use of much off-the-shelf equipment while still giving the properties of a system meeting practical data requirements For example modems are commercially available to produce a baseband PSK binary data stream which can then be modulated onto a video carrier These modems can produce a 0 dbmv signal on a 75 ohm line with good capture properties and excellent phase stability The off-the-shelf modem will probably have poor acquisition time on order of 100 milliseconds which will limit the system to less than two hundred terminals in initial experiments Later experiments can be performed with 4 level DPSK and at a Megabit sec data rate However the short acquisition times required for 1 Megabit sec data rate would require special development of a Surface Acoustic Wave Device type detector Matthaei 1973 The final selection of parameters for a practical data transmission system depends upon several variables whose values are uncertain and subject to change with improvements in technology 1 The bandwidth of the head end minicomputer 2 The amount of core at the head end minicomputer 3 The bandwidth of the links to external test facilities 4 The throughput at the terminals 5 The subscriber saturation level of CATV system The specifications to be met by the final modems are given in Table 8 3 1 13 47 jjMulliBiiiiiMS „ ■„■m »« rieiworR Analysis crporanon MODEM SPECIFICATIONS type of modulation data throughput carrier frequency nominal signal level impedance reflection coefficient noise figure power hum DPSK 100 KB sec or IMB sec 5-240 MHZ input 10 dbmv output 32 dbmV 75fi -23 db 7 5 db 60 db below signal level Table 8 3 1 Modems meeting these specifications are available with performance parameters and resulting system degradation indicated in Table 8 3 2 Cuccia 1973 The signal degradation is within -20 acceptable limits for error rates better than 10 ±3 48 Mito'ii'i infill r msmuämäälmmuäm ■--■ ■ ■■■■'■■-» ■- _ __ _ Network Analysis Corporation MODULATOR Carrier Instability in Carrier Source 1 2° RMS in a PLL with Bandwidth 0 03% Bit Rate Bandwidth Static Phase Error in QPSK Modulator 0 05 db 0 10 db Rise Time in Each Phase Change 1 4 Bit Period 0 40 db Amplitude Unbalance in OPSK Modulator 0 2 db 10° db 0 10 db Data Asymmetry from Data Source 2% 0 05 db Group Delay Distortion Modulator 25° 0 20 db Clock Instability 1° RMS in the Bit Synchronizer PLL 0 10 db SOURCE TOTAL 1 00 db DEMODULATOR Incidental FM from all Oscillators in RF Channel and Carrier Reconstruction 1 2° RMS in PLL with Bandwidth 0 03% of Bit Rate Bandwidth 0 05 db Static Phase Error in QPSK Demodulator 0 10 db Reference Phase Noise in Reference PLO 0 10 db Total Group Depay Distortion Total Channel from Modulator 20a 0 35 db Timing Jitter in Matched Filter Sampler 4% 0 25 db 1 5% 0 15 db 4% 0 10 db Timing Bias Error in Matched Filter Sampler DC OffseJs-Total Receive Data Waveform Matched Filter De Lector Mismatch Table 8 3 2 13 49 1j i»» m feJi J 0 60 db SOURCE TOTAL 1 7Ö db Network Analysis Corporation 8 4 A TEST MINICOMPUTER General The minicomputer used as the test head end controller in the Terminal MATV-CATV system vill have the following characteristics A B C 16 bit word length vi y sec cycle time core memory Memory size expandable to at least 32k words In order to adequately test the Terminal TV System a variety of peripherals and interfaces provided by the mini computer vendor may be required In addition several custom interfaces may have to be developed for cases where standard interfaces are not available B Data Rate Constraints The data rates expected in the head end computer system are shown in Figure 8 4 The data to and from the cable modem will flow at the rates of either 10 or 10 bits per second although the flow will net be continuous in general At the rate of 10 bits second a 16 bi computer word will be assembled in the interface every 16 y seconds The transfers of these words into and out of the computer will require the availability of a high speed data channel or alternately a Direct Memory Access DMA channel as a required option on the computer Transfers to and from memory will be accomplished automatically without requiring program intervention 13 50 ■-■■■■■ Network Analysis Corporation as o O U 0 U 10 0 •P •H V ■P •H J3 s B vD vD Q M 0 0 u w u s s « •p 0 Q u w 9 £ 2 H e B B Q En 1 w II 8 £ B ti Ü a' 8 H M s co 23 a 1 o H Cn -H w B w del 2 H 2 Hi B H B B en H H B fa ft So 13 51 Network Analysis Corporation C Functional Description The computer at the head end must implement the programs to test the following functions for the system o Buffering of packets to and from terminals • Flow control of cable syst-K • Implementation of netw • protoco The headend computer will provi'le sufficient Lui ei storage to match the difference between the pea» to aver - ata rates seen on the cable system and any external sources of data Initially storage for a total of the order of 100 packets will be provided The head end computer will provide the required cable system flow control by means of acknowledges for received packets When traffic from the cable terminals begins to congest the system the head end will effect the flow control by refusing to acknowledge packets which cannot be accepted This will cause the terminal to retransmit messages producing the same effect as errors on the cable system» The head end computer will provide the implementation of all protocols required to communicate on the system The following is a list of some of the major program pieces which must be implemented 1 Cable modem interface handler 2 Special interface to external facili es handler 3 Monitor or supervisor for system 4 Cable flow control routine 5 Buffer allocation and management 6 Miscellaneous background tasks such as garbage collect timeouts accounting etc 13 52 _ _______ Network Analysis Corporation 8 5 MINICOMPUTER TO CATV INTERFACE This specification describes the interface between the head end computer and the MATV and or CATV system system is shown in Figure 8 5 1 A diagram of the FUNCTIONAL SPECIFICATIONS A The MATV-CATV computer interface will use a non-slotted ALOHA random access mode The first transmission as well as subsequent retransmission of messages will be randomized over time B The interface will be able to simultaneously and independencly transmit to and receive data from a suitable modem at a rate of 100K or IM bits per second Data will be supplied to and received from the modem in bit serial form The interface will be able to provide crystal controlled clock signals to the modem and receive modem clock signals along with modem data C The interface 8 bit characters The actual number of valid character on a message will be capable of receiving or transmitting computer program shall be able to control the character bits in each received or transmitted by message basis D The interface will be capable of transparently receiving or transmitting all bits included in each character including a parity bit independently for transmitter and receiver E The following formats will be used for the TV Terminal system 1 Data Packets HEADER 1 TEXT CHECKSUM 2 Acknowledge Packets HEADER CHECKSUM The format within the header will be as follows DEST I D 1 40 bits SOURCE I D 4 0 bits CONTROL CODES 8 bits 13 53 MESSAGE NUMBER 4 bits TERMINAL RCVR RATE 4 bits COMPUTER TO TV TERMINAL CABLE SYSTEM INTERFACE TEST INTERFACE TO MINICOMPUTER CABLE SYSTEM MODEM CABLE TO TERMINALS CABLE FROM TERMINALS FIGURE 8 5 1 13 54 Network Analysis Corporvtion The field sizes are chosen to allow expansion to a reasonable number of terminal sufficient control source I D fields lowest 16 bit word interfaces on a given TV system and to provide codes tor system operation The destination and will each be 40 bits long This length is the boundary which will contain the temporary 36 bit source and destination identifier F manner The transmitter section will operate in th'j following 1 Messages within the computer which are to be transmitted will be placed in one of two queues a high priority acknowledgement queue or a regular message queue 2 All messages in the high priority queue will be transmitted before any regular messages are sent The high priority queue will be serviced before each regular message transmission 3 Copies of transmitted acknowledgements will not be kept since acknowledgements are never retransmitted 4 Copies of all transmitted regular messages will be kept in the computer until either receipt of an acknowledgement from the destination or the occurrence of a program-determined number of unsuccessful retransmissions 5 The transmitter program will set up a parameter table for each terminal active on the cable system This table will contain terminal-specific information such as terminal output rate and cnaracter set and will be used to format each transmitted message to match the characteristics of the destination terminal and to allow the spacing of messages for each specific terminal in time to match terminal output speed 6 The transmitter program will operate in the computer in conjunction with other programs which will deal with the various functions required of the head end test mini computer system There will be a monitor or executive program which will control the activities of 13 55 Network Analysis Corporation the cable system and external interface programs This monitor will also control or provide various required console related activities and accounting functions 7 Transfer of messages from the computer to the interface logi _ will be by Direct Memory Access DMA of the head end computer 8 The transmitter interface hardware will calculate the message checksum for each message and append it to the message In addition the hardware will automatically perform such routine tasks as synchronization character generation special escape character generation for transparency and others as required When the interface hardware completes the transmission of each message a program interrupt will he generated G The receiver section will operate in the following manner 1 Message transfers between the cable system interface and the computer memory will be by means of DMA 2 The interface logic will compute the checksum of the received message and notify the computer by interrupt if an error has occurred In this case the computer program will discard the data for that message 3 The interface logic will automatically acquire character synchronization ana will strip synchronization and control characters from the input data stream 4 Tie interface will allow the transoarent reception of full binary text 5 As each messaae is received its checksum will be verified and a computer interrupt will be generated 6 The receiver section of the computer program will upon notification by a receiver interrupt examine the new message and dispatch the message to the appropriate queue for further action Sample actions are given below a New message - determine destination queue and forward message send acknowledgement to terminal and check for retransmission 13 5 1 1 Network Analysis Corporation b c Acknowledge - remove copy of acknowledged message from transmitter retransmission storage Duplicate - discard 7 The receiver section of the program will operate under the control or the computer monitor program and will interface to the transmitter and protocol programs 13 57 Network Aralysis Corporation ELECTRICAL SPECIFICATIONS A Modem Connection The interface will be designed to match the choice of modem Interface circuits should prevent or minimize damage to either the computer or the modem under conditions of short circuit open circuit or voltage or current transients State-of-the-art isolation techniques will be used including optically-coupled circuits and protective diodes on sensitive elements B Computer Connection The interface will be designed to connect to the Input Output bus of the head end computer The manufacturer's recommendations and specifications will be met in all cases to insure proper computer and interface operation C Power Power for the interface logic will be obtained from the computer power supply Power for circuits beyond the isolation devices will be obtained by small modular power supplies which will be incorporated into the interface assembly D Logical Design The logical design of the interface will be realized using standard integrated circuits and components either of the types recommended by the minicomputer manufacturer or their equivalent The project will result in a reliable cost effective interface with sufficient flexibility to allow reasonable system modifications during testing 13 58 Network Analysis Corporation MECHANICAL SPECIFICATION A The interface will be packaged on circuit boards of the type used by the minicomputer for interface circuits The circuit boards will plug into the I O bus of the minicomputer in the enclosure provided by the minicomputer and will connect to the modem with a cable and connector Estimated weight of the interface is less than 10 lbs The prototype version of the interface will most likely use wire-wrapped sockets for the integrated circuits to facilitate design changes during testing B There will be no operational controls associated with the interface other than program control Test modes and switches for their control will be provided 13 59 Network Analysis Corporation BLOCK DIAGRAM OF MINICOMPUTER TO CATV INTERFACE Figure 8 5 2 Assume that any frequency or phase acquisition is accomplished by the modem The received bit stream is examined by the interface hardware for sync characters and synchronization is automatically accomplished without computer intervention The interface hardware also handles DLE doubling and other special signaling conventions such as STX detection and ETX detection on the cable system automatically As each character is received it is packed into a minicomputer 16 bit word and when the 16 bits are ready the word is transferred to core memory on a DMA cycle stealing basis A computer interrupt is generated at the end of a packet or upon an error condition The transmit section of the interface is also automatic in that after initialization of the interface for a new packet all communication discipline is accomplished automatically by the interface hardware and words of data are simply requested by the interface via DMA from core unpacked and serialized The hardware also calculates and appends the checksum 13 60 Network Analysis Corporation c es E- T J K z E- o e a c K C 11 fc es u Hi u Q E- «• E- s c t- c u CT S C U EX CC8 t r f o t_ Zh C o c o C o a tu u t 2 U h • US u 1 U es c T IT U ua I J tu es - tu tu W O X K U ►J E- es £- u M U O u so «w H y ei ED es H ft z 7 O M O o o U J ca w U C c Ec u E-i D C o u O tu Q tu o er tu M £- u sca O in cd o u 1 ü 13 61 Network Analysis Corporation 8 6 MINICOMPUTER TO EXTERNAL TEST FACILITIES INTKMFACL This specification describes the interface between the head end test minicomputer and a communications link to external test facilities Functional Specifications A The interface will communicate with the external test facilities over leased lines using commercially avai able modems and will provide all of the control signals required to operate these modems B The interface wiln connect to the I O system of the selected minicomputer and will comply with all specifications set forth for such connections C The interface will operate in full duplex mode at a rate of up to at least 4800 bits per second Electrical Specifications A The interface will be able to connect to a suitable data modem operating at 4800 bps full duplex The connections will conform to EIA RS-232-C The interface will incorporate adequate isolation features to prevent damage to itself or to the modem under conditions of short circuit or open circuit signal leads In addition sensitive interface elements will be protected from damage by voltage or current transients from external sources B Power Supplies The interface will be powered from the minicomputer logic power supplies except for circuits which are to be isolated from the computer system Any isolated sections of interface logic circuits will be powered by isolated power supplies with characteristics to match the degree of isolation desired It is estimated that less than 50 watts of DC power will be required for the interface circuit - 13 62 Network Analysis Corporation C Logic Realization The logical design of the interface will be realized using standard integrated circuits and components The minicomputer vendor's recommendations of logic elements and design techniques will be followed especially those related to I O bus loading driving and termination At the present time it appears possible that a standard vendor Synchronous Line Controller will be adequate for the job at hand Mechanical Specifications The interface will be packaged on plug-in circuit boards which conform to minicomputer vendor I O board specifications The interface will be housed in the minicomputer I O enclosure There will be no operational controls or indicators for the interface However test switches and indicators will be provided as required for troubleshooting The modem will connect to the interface via a cable assembly which will run from the socket of the logic board to a suitable connector mounting panel 13 63 Network Analysis Corporation 9 SYSTEM TESTS In addition to testing the various digital devices extensive testing must be performed to demonstrate the viability of data transmission on MATV and CATV systems Data users may find cable system reliability quite poor when compared with the common carrier facilities that they are used to One of the major problems with data transmission on MAI and CATV s stems is that there is virtually no redundancy in these systems Most present systems do not even have standby primary power Alternate routings are not available in case of system castrophe There are no Government or industry minimal standards for acceptable performance hence performance will vary from system to system Many old systems were built to extremely loc Q -pecifications on noise and cross-modulation and have serious reflection problems because of the use of unmatched subscriber taps Fortunately systems in large cities and new buildirgs are much newer and are required to meet more exacting standards Even with these systems the construction norms are still those which satisfy casual TV viewers not data users Thus loose connections and cracked cable sheaths cause intermittant transmission conditions and momentary disconnects These would cause only minor flashes on a TV picture but constitute major data dropouts in a high speed data circuit Cable connections often loosen under the influence of vibration and the cold-flow property f aluminum Strong RF sources such as nearby mobile radio transmitters amateur radio transmitters and AM and short wave broadcasting stations leak into both upstream and downstream cables and interfere with the low level television and data signals Switzer 1972 Finally systems are tested haphazardly and hence in some parts of a CATV system noise and cross-modulation levels may not meet written system specifications The limiting factor in determining the performance of the system will not be Gaussian noise interference but a number of practical factors which pro- 13 64 j I § I i Network Analysis Corporation vide interference generally categorized as impulse noise These - ctors are difficult to characterize and includr phenomena such as loose connections cracked cable sheaths a id R-F leaks Hence we must run tests on an actual CATV system to evaluate system performance Tests should be conducted in three phases The first phase consists of the tests necessary to verify operation of the MATV system The second phase should measure the performance of the MATV system under conditions of simultaneous video and data communications Tests should be made to determine the interactions between the video and data signals The third phase of testing should measure the characteristics of data transmission on the MATV system Verification of MATV System Operation The testing of the completed MATV System involves a standard set of well documented procedures which fall into the following general categories 1 2 Balancing the head end A Check signals at antennas and align antennas B Adjust amplifier output levels gains AGC and tilt C Tune sound traps D Record all settings and signal levels Testing ai1 lines A Verify proper installation of each line without short cr open circuits 3 B Verify proper terminations of each line C Verify proper signal reception at each tap Check picture quality A Perform visual check of signals 1 windshield wiper effect caused by excessive cross modulation 2 snow caused by low signal to noise ratio 13 65 Network Analysis Corporation 3 beats caused by overloads mistuned trap filters or improper sound eerier levels in adjacent channels 4 ghosts caused by improperly terminated lines or direct pickup of signals 5 B hum bars caused by 60 cycle pickup Measure cross-modulation second order distortion and carrier to noise ratio C Compare pictures delivered throughout system with those obtained directly at the antennas These tests will not all be necessary for the CATV system if it is an already tested operational system Some measurements should be made to record actual system parameters The next step is to establish the digital characteristics of the MATV or CATV system The following tests should be run first on the MiTV system and second on an actual CATV system The UA- Columbia CATV system in Brookhaven Long Island has given permission to run such tests he tests should be run first with packets from a single terminal only and then with simulated background traffic from multiple terminals Performance of MATV System with Digital and Video Signals 9 1 Find data error rate as a function of the level of the data signal relative to combinations of the TV channel carrier levels on the cables with and without extender amplifiers i e short term error rate 13 66 Network Analysis Corporation 9 2 Test visual interference into the television channels and the relation of this interference to bit patterns i e random data or repeating pattern Tests should be configured to maximize interference so that test can be considered worst case tests Hopefully interference will only be visible at levels far above that which will result in satisfactory error rates for the data system 9 3 Based on short term data from tests under 9 1 above set the operating level at some reasonable short term error rate for example 10-7 and operate the system for at least a l-to-2 week period of time and record the long term error statistics After a period of test of l-to-2 weeks it may be desirable to reset the level and repeat these relatively long term tests The purpose of this test is to determine whether error statistics vary significantly during the day or are related to other factors such as weather If impulsive noise type interference is seen then it would probably be wise to repeat the test at a number of different levels to determine to what extent the operating level affects error statistics In order to minimize the data reduction and other labor needed for these long term tests data will be recorded digitally in a manner that is adaptable to computer processing 13 67 Network Analysis Corporation Performance of Digital Data Transmission System The tests of the Digital Data Transmission System fall into two categories initial simple tests to debug components of the system and verify system operation and system performance tests Testing of system components proceeds to a lar e degree as a part of component development Listed below roughly in order of complexity»are the tests which will be performed These tests will be carried out under typical and worst case combinations of video signals on the cable systems 1 Single Terminal With Data Path Through MATV System For these tests the terminal interface will be configured so that it can receive its own transmitted packets and an upstream-to-downstream converter will provide a data loop at the head end of the MATV system Figure 9 1 The tests will verify the operation of the interface on the cable system In addition several intermediate signal or data looping arrangements such as modem analog loop at baseband digital loop at modem input and digital loop at interface input and output will be tested to develop trouble diagnostic aids Several tesns will be perform- ed to insure that different terminals located separately on the MATV system can communicate with each other 2 Mini Computer Tests With Data Path Through MATV System The mini computer will be connected to the cable system configured for the data loop from d' nstream to upstream Figure 9 2 13 68 It V Ir -' Network Analysis Corpaatkm will be tested to verify operation of the computer the computer interfaces and modems by sending packets to itself In addition error rate measurements will be made using the computer to generate data and record the test results Receiver acquisition time will also be measured 3 Initial Data System Tests The mini computer and a small number of TV terminal interfaces will be connected to the MATV system Figure 9 3 Operation of the system will be verified and human factors such as delay and convenience will be checked for acceptibility Test messages will be passed between th terminals and the head end computer and vice versa 4 Traffic Simulation The mini computer and a number of TV terminal interfaces will be connected to the MATV system Figure 9 4 The mini computer will provide data to the terminal inter- faces to simulate the effect of a large number of terminals using the system The computer will be used to generate test messages and interfering traffic System data throughput transmission delay and number of retransmissions will be measured as a function of number of terminals active 5 Operation of System With External Data Sources The head end mini computer will be connected to external test facilities Figure 9 3 and the performance of the entire data transmission system will be verified under typical user situations These tests will involve users at individual terminals performing operations representative of actual terminal use 13 69 Network Analysis Corporation rr- MATV SYSTEM aj h r Converter to loop Modem Head End from upstream to down Possible Diagnostic Loops e Modem analog loop at baseband b Digital Loop at modem input c Digital Loop at interface output d Digital loop at interface input Figure 9 1 c d r Test 1 13 70 Termina Interfaq« Terminal Network Analysis Corporation MATV SYSTEM DOWNSTREAM HEAD END I UPSTREAM MINI-COMPUTER AND INTERFACES AND MODEMS Figure 9 2 Test 2 13 71 F IEQ CONVERTER TO LOOP DOWN TO UP t r Network Analysis Corporation -ÜH- MATV SYSTEM DOWNSTREAM HEAD END f UPSTREAM n 1 MINI-COMPUTER AND INTERFACE AND MODEM I I i I I TERMINAL MODEM AND INTERFACE USER TO EXTERNAL TEST FACILITIES Figure 9 3 Test 3 13 72 r TERMINAL MODEM AND INTERFACE USER Network Analysts Corporation AÜU MATV SYSTEM HEAD END i •s DOWNSTREAM UPSTREAM MINI-COMPUTER INTERFACES AND MODEM r I INTERFACE AND MODEM TEST DATA T INTERFERING DATA TRAFFIC Figure 9 4 Test 4 13 73 INTERFACE AND MODEM Network Analysis Corporation 10 CONCLUSION An investigation of all aspects of the use of MATV and CATV systems for interactive packet transmission has led to the conclusion that the operation is feasible and appears to offer an excellent high bandwidth method for local distribution The characteristics of the MATV and CATV systems are such that they would form a highly favorable environment for data transmission Detailed specification and study of the required modems and digital equipment indicate that the devices can be built to meet reasonable component specifications and to meet overall system requirements It is also clear that the techniques and some of the components which are used to solve the local transmission problem mentioned above may be applied to solve communications problems in other areas most notably for military applications I Military Installations A Existing Wiring Systems The techniques of converting terminal data to packets at the terminal and transmitting and receiving those packets on shared channels can be applied to existing wiring systems such as 13 74 Network Analysis Corporation twisted pair networks In the case of utilizing an existing wiring system the performance of the entire terminal-computer system would depend on the bandwidth of the wire transmission medium and the distances involved In the case of twisted pairs for instance modu- lation of terminal signals tc VHF would be unnecessary and unworkable but low-level standard signalling could be used on such a system In certain cases where distance could be gained at a sacrifice in bandwidth low frequency audio modems could be used and operation would be quite similar to operation of Remote Job Entry RJE terminals on a multi-drop telephone line One of the major differences between a cable system configuration and an existing twisted-pair network configuration is that the cable system generally tends to be a tree structure while the twJsted pair network usually has a star structure although tree structures are also used This difference can easily be surmounted by connecting all wires of the star together at some point even the center The important point is that all signals from all terminals be available on the same channel or pair The trade-off in this case is that instead of having the available system bandwidth of the sum of the bandwidths of all lines the effective bandwidth is reduced to that of a single line This effect will have to be evaluated for each potential use B New Installations A detailed analysis of the requirements of each new in- 13 75 Network Analysis Corporation stallation will be essential to determine the choice of type of data transmission system to be implemented Both coaxial cable and twisted pair systems have advantages and disadvantages scne of v i irh are listed below 1 2 3 4 Twisted Pair - Advantages a Relatively low cost of wire b Non-critical installation c Terminal connection is simple no special interface required Twisted Pair - Disadvantages a Low bandwidth therefore expansion is limited b High noise pickup c Data easily eavesdropped d In star networks high cost of switch at star center e Physically large cable bundles requiring large conduit space f Limited signalling distance Coaxial Cable - Advantages a Extremely wide bandwidth - virtually unlimited expansion b High noise immunity c Relatively inexpensive head end switch d Single cable requires little physical conduit space e Longer distances allowed due to modulation Coaxial Cable - Disadvantages a Higher cable cost - system components cost 13 76 Network Analysis Corporation b Installation relatively more difficult technically c Higher terminal equipment cost In those situations where large numbers of terminals are to be used and easy expansion to larger numbers is important the advantages of a coaxial cable system are probably enough greater than those of a twisted pair system to justify the choice of the coaxial system on that basis alone II Tactical Radio and Satellite Communications The solution of the local distribution problem will be based upon the use of an existing or readily obtainable channel for communication namely a coaxial cable However the equipment which will be used in the solution will not in general depend on the channel used so long as the transmission properties or channel characteristics do not change significantly The cable represents an almost ideal channel in the serse that there is no multipath although there are reflections from mismatches and the cable is a much more controlled environment from the standpoint of external moise sources for instance than a radio channel However in the situations where an alternate channel has sufficiently good characteristics it is possible to use the same approach and hardware with minor modifications such as replacement of the modems with units capable of operating on the new channel frequencies or the addition of radio transmitters and receivers on the new channel 13 77 Network Analysis Corporation A point to point tactical radio system is one such example The ALOHA system has proven the viability of the technique on a radio channel It would thus be possible to use the equipment built for a cable system wich an additional transmitter and receiver on a radio channel A similar channel which would be very close to a cable is satellite link to a tactical terminal A tactical station with a small antenna transmitter and receiver could set up a channel good enough to communicate with a central computer The characteristics of the system which make it attractive for tactical command and control situations are the shared use of a limited resource namely spectrum Several examples of such situations might be 1 Army battlefield reporting inputs to data bases outputs from data bases 2 Shipboard use between ships - allows several ships to share the data base of each Another advantage of the cable type of system is that data can be encrypted fairly easily between the terminal and interface It is also possible to randomize frequencies of transmission and reception by periodically sending frequency shift packets which defines a new set of channel frequencies The Positive acknowledge- ment scheme used in the TV Terminal rystem is ideal for tactical Command and Control data transmissions in a jammed environment 13 78 Network Analysis Corporation 11 APPENDIX A CALCULATION OF ERROR RATES FOR CATV SYSTEM For the sake of illustration we will consider noncoherent frequency shift keying FSK The error rates for coherent detection or phase shift keying of course would be even lower Schwartz et al 1966 Let S N N Signal Power Noise power Cross modulation noise power N Thermal noise power t T Average synchronization error time Bit width time Then the signal to noise ratio is S N 1± N N c r Nc S Nr S where 1 - - 2tx2 q 1 Let Pe be the bit rate error probability Let m be the number of keying frequencies in a multiple FSK System Then Schwartz et al 1966 - S N „ i m-l 2 Pe 5 1 e m We assume that each packet carries its own synchronizing bit and hence there is no need to synchronize overy terminal to a master clock Therefore temperature pressure and humidity variations which have approximately the same effects at all frequencies do not enter into the calcualtion of t The group delay variation over a six Megahertz bandwidth is For a 1 Megabit pulse rate Hence q 36 Using thes probabilities in Table 5 1 less than 2 y seconds Roger ess 1972 T 1 p second and t 2 y second formulas and numbers we have the error for the Boston complex 13 79 Network Analysis Corporation Consideration of reflections intersymbol interference and 60 cycle hum also lead to the conclusion that MATV systems and CATV systems are excellent media for packet data transmission Intersymbol Interference The signal levels in a CATV system are controlled via AGC and dual pilot carriers Ripples are kept to less than 1 db over the whole frequency band In any case frequency shift keying is insensitive to small amplitude variations The effect of group delay error has already been taken into account in the use of q in the formu'1 for error probability The remaining source of intersymbol interference is the reflection of pulses and the effect of the reflected pulses on the transmitted data There are three types of disturbances due to reflections In each case we shall see that video restrictions are certainly stringent enough to avoid any difficulties for data transmission 1 Periodic changes of minute magnitude uniformly distrib- uted along the cable length the magnitude of changes being essentially equal from period to period due to the nature of the manufacturing process cause reflections which add in phase at certain frequencies The signal strength relationship of the reflected wave to the incident wave is referred to as structural return loss SRL Typical values for the magnitude of SRL are better than -26db Olszewski and Lübars 1970 Assuming that the reflected signal is always of an opposite sign to the original signal the signal level is degraded by at most S-a where a is the amplitude of the reflected signal The signal-to-noise ratio becomes BTL 1971 13 80 Network Analysis Corporation S-a N _ s i_ a y N In other words S IT is degraded by 1- -§- S For a reflected signal of -26db 1- _§_ S is 9975 Hence the reflection problem is completely under control 2 A localized change or changes on the cable cause echo phenomena Low reflection coefficients of active and passive devices and the use of directional couplers at all subscriber taps ensure that the magnitudes of reflected pulses are in the no ghost range of Figure Al Shekel 1962 Mertz 1953 Rheinfelder 1970 These are translated into critical distances for dif rent types of cable in Figure A2 Thus for example considering the reflection on 412 inch cable at Civ inel 13 the critical distance is about 250 feet and the ratio of the magnitude of the reflected signal to the magnitude of the original signal is -23db 3 Randomly distributed changes of random magnitude which persist throughout the cable length cause reflections which do not add in phase These can be taken into account in noise calculations and are usually negligible 13 81 Network Analysis Corporation J_ -• GHOST VISIBLE -fft o 2 M IC «OST5 ■» 2 r 2 3 -49 •• - 1 M M M «M 1000 MM MW It TIME DELAY IN NANOSECONDS FIGURE Al Curve showing perceptibility of ghosts 70 100 200 500 700 1000 DISTANCE FROM POINT OF MISMATCH IN FEET FIGURE A2 Graph for determination of critical cable lengths 13 82 10000 Network Analysis Corporation Interference from Power Frequencies Cable system amplifiers are powered by low voltage 60 Hz power through the co-axial cable This power may be as high as 60 volts RMS and currents may run to 10 amperes RMS with peak currents even higher There are significant harmonics of the power line frequencies present Some amplifiers use switching mode power supplies with switching frequencies in the 10-20 KHz range Hash from these svitching regulators also finds its way into the cable However both the 60 cycle harmonics and hash limit only the area of very low frequencies which are generally avoided for data transmission anyway 13 83 Network Analysis Corporation 12 APPENDIX B MAXIMUM NUMBER OF ACTIVE TERMINALS In a CATV System there are separate channels allocated for upstream and downstream messages Since the responses are longer and more frequent than the inquiries they will limit the number of terminals For integers w x y z lat 450 w packet size no of hits packet 2x rate of messages no of responses hr 4y message size number of packets response 1 x -10 z pulse duration seconds At a 1 Megabit sec rate is 1 z 1 and the pulse duration use on a binary system Note that the number of bits second is 450W 3600X 4y WXy which we define as 0- Then the number of packets second for each terminal is x -ta3600 At a 3 Megabit sec rate the pulse duration is 33 The corresponding average packet duration is T zw 4 50 x 10 6 seconds 13 84 seconds Network Analysis Corporation The maximum number of active users per trunk in a system is given by Abramson 1970 k-max f°r — an unslotted system and T»axes CAT for a slotted system In other words the bandwidth of an AIOHA type interactive channel is effectively reduced by a factor of 2e for an unslotted system and a factor of e for a slotted system Hence k maxu -JL600 x 106 2e «3600 wxyz 184 xlQ6 ßz Similarly k max0 »368 x 106 13 85 Network Analysis Corporation 13 APPENDIX C FORMULAS FOR TRAFFIC IN LINKS In order to precisely formulate the traffic requirements throughout the network it is convenient to introduce some elementary descriptive terminology from graph theory We define a set of points called nodes to represent the head end junction points router converter concentrator multiplexer and bridger locations The nodes are represented by integers 0 for the head end and 1 to n for the remaining nodes where the total number of nodes is n 1 The transmission system including amplifiers and any single or dual cable joining two points corresponding to nodes a and b is represented by an undirected arc a b The arcs and nodes together comprise a graph G N A where N is the set of nodes and is the set of arcs G is a tree in our case that is a graph joining all nodes and containing no cycles Let P be the path in G from node i to node j that is the sequence of nodes and arcs listed in order in tracing a route from i to j If node 0 is the head end then path PQ is a path from the haad end to node k If node i precedes node j in PQ we say that nod« i is upstream of node j and node j is downstream of node i i u j j d i Let k d j and i d k or i k then we write i d j k D j k i i d j k Let D j be the set of all downstream points of j D j i j d i 13 86 Network Analysis Corporation Let A x B be the cartesian product of the sets A and B that is A x B j a b aGA bCß Let I a b be the number of inquiries originating at node a addressed to node b Let R a b be the number of responses originating at node a addressed to node b Then define I A B Z-r Ka b a b C AxB R A B 2 i R afb a b C AxB M A B I A B R A B EXAMPLE Figure c1 13 87 Network Analysis Corporation N O 1 2 3 4 5 6 7 2 u 3 2 u l 2 u l 3 D l 3 2 6 l D l J2 3 4 5 6 7 For A 4 5 and B J2 3J M A B 1 4 2 1 4 3 1 5 2 1 5 3 R 4 2 R 5 3 R 5 2 R 5 3 13 88 Network Analyst Corporation In this section we present formulae for the link traffic in terras of the location of concentrators multiplexers converters and routers We first assume there are only converters and routers We use the notation developed in Appendix C with intuitive explanations of the significance of the notation Let us consider the arbitrary junction in the network and designate it by the integer i We are interested in the traffic in links downstream from i There are three cases to consider A There is local routing at i B There is forward routing at L C There is no routing at i The notation used is defined precisely in the terminology of graph theory in Appendix C A simple intuitive explanation is given in this section We assign the integer 0 to represent the head end and we assign a unique integer to every junction bridger multiplexer concentrator and converter location in the system Let N represent the integers corresponding to all these locations We wish to consider the traffic in a specific link downstream from the integer i representing the junction under consideration Let i' represent the integer corresponding to the first point downstream from i We wish to know the traffic in the link between i and i1 i i' Th traffic in i i' depends upon the local routers downstream from i and the forward routers upstream from i We therefore introduce some special terminology to represent these points Trace any path from i in the downstream direction so the path contains i' The first local router on this path aside from i itself is designated ■ n where It is th number of the point at which the router is located If there is no local router on the path then the last point on the path is called t n Next trace the path from i upstream to the head end let r be the first forward router encountered Let r1 be the first l i point downstream of r on the path As an example of this terminology i r r' t and t _ are shown in one case in Figure C2 Note Bridgers are amplifiers which feed into feeder cable from which customer taps and drop lines emenate 13 89 Network Analysis Corporation in particular that even if point e is a local router it is not and even if point d is a forward router it is not labelled t l e labelled r Figure C2 We next introduce some general terminology to be able to describe sets of points downstream from specified points along possibly specified paths Let D a a be all points in N downstream of a on the paths containing a' Let D a be all points in N downstream from a For sets of points A and B chosen from N I A x B is the number of inquiries directed from terminals led from bridgers in A to terminals fed by bridgers in B and R A x B the number of responses directed from points in A to points in B The total number of messages is M A B I A B R A B Thus for example M N x D i i' is the number of messages directed from any point to any point upstream of i on the route containing the router or terminating bridc er i' Finally we assume NQ 0 where the head end is point 0 M N-N- that is all points except the head end N N that is all points 13 90 Network Analysis Corporation Then for y 0 the expressions below give the usage of link i i'l due to central traffic For y l the expressions below give the usage of link i i'l due to local traffic For y t the expressions use the total traffic to and from all nodes N including central traffic and local traffic We first give the expressions in the case in which there are no converters Then all forward messages are at w and all reverse messages are at w Regardless of the routing at i the traffic in the reverse link i i' is given by M D i i' x N -£ M D ti xD t j C la The expression M D t a x D t Q is the local traffic which is prevented by the router at t n from appearing upstrsam of t n The summation gives all such traffic from all local routers downstream of points along the path containing the link i i' Since this summation appaars repeatedly we introduce an abbreviation for it L i i' to indicate the local traffic downstream from i and i' which does not reach i Rewriting C la we then have M D i i' x N - L i il » £ lb The traffic in the forward ink i i' is given for the three cases by the following expressions A Local Routing at i M Ny x D ri r'i - L i i' G 2 13 91 Network Analysis Corporation B Forward Routing at i M N C x D i i' - L i i' C 3 No Routing at i C4 M Ny x Dtr r' - L i i' As an example of the use of the notation for y 0 the expression in C l indicates that the traffic in the reverse link is given by the inquiries from the terminals downstream from i on the routes contains i' directed to the head end plus the responses directed from the same terminals to the head end less the inquiries and responses directed from terminals downstream of t ü to other terminals downstream ot t We now consider the addition of converters For links which are downstream of converters all messages are at u and «f and the above formulae are unchanged For the remaining links messages are carried at w u' w_ and w'f and the formulae must be modified The expressions below give the traffic in link i i' at the frequencies »' and w'f We introduce a terminology for concentrators similar to that used for local routers Trace any path from i in the downstream direction so the path contains i1 The first concentrator is called c a if it i« located at point Regardless of the routing at i the traffic in the reverse link i i' at w' is TM D C a ' x N y - 2-f Lt 'i b is downstream of a concentrator c i c £ M D c xD t 1 im J is downstream ' ' i a of t i b 13 92 M D t x D ti b fb ' c# 5a Network Analysis Corporation The terms in brackets give the local traffic which does not reach the link i i J because of a local router at t fa The expression is more complicated than before becavse the concentrator may be in two different positions with respect to the router The first summation in brackets corresponds to the situation in Figure C3 a where the router is downstream of the concentrator The second summation corresponds to the situation in Figure C3 b where the concentrator is downstream of the router i a a Since the term in brackets appears repeatedly we introduce an abbreviation Jbreviation for it L i i' the local traffic with concentrators Rewriting C5a we have £ M D cifa X N - Lc i i' C 5b The traffic at w' in the forward link i i' is given by the expressions below In these expressions AO B denotes the points common to A and B A Local Routing at i EM N y x D c l a nD r r' -L c i i' l 13 93 C 6 Network Analysis Corporation B Forward Routing at i y M N x D c 3 0 D i i' - L c i i' j y i» C C 7 No Routing at i EM N x D c D D r r' - L i i' fc 8 To obtain the traffic in these lines at wr and «f subtract the expressions in C 6 - C 8 from the corresponding expressions in C 2 - C 4 The effect of multiplexing at converters is to increase the data rate at w' and »• The effect of concentration at the converters is to isolate the links feeding upstream into the concentrator that is each line operates separately at the low data rate and their combined traffic is handled only at the higher data rate 13 94 Network Analysis Corporation 14 APPENDIX D DESIGN OF BOSTON SYSTEM To determine the usefulness of the various options ond devices we have considered we will apply them to the design of an interactive packet data system for Medford Massachusetts a section of the Boston CATV complex In Figure D l b a branch of the trunk is drawn for Medford Massachusetts The triangles represent bridger amplifiers These amplifiers feed into feeder cable and extender amplifiers with customer taps and drop lines emanating from the feeder cable In the design for Medford the feederbacker arrangement is used so that the trunk lines are dual cable and the amplifiers are two-way units as shown in Figure 4 4 The hexagons represent local origination stations The feeder system emanating from a given bridger amplifier is called a cluster The number next to each amplifier gives the number of terminals in the cluster associated with that amplifier The average number of terminals per cluster is 137 with complete coverage of all homes We now consider the design of the Boston interactive packet cable system by focusing our attention on one trunk in the Medford area We assume that the average traffic per terminal is 40 bits sec We conservatively assume that this is the rate for inquiries as well as responses We assume that in the design the data from the terminals is 100 kilobits sec the upconverted rate is 1 Megabit sec In appendix B we obtained the results in Table D l showing the number of active terminals that can be supported on a trunk at each data rate type of da ta vjs tern rate slotted system 1 Megabit sec 100Kilobit sec Table D l unslotted system 9 000 4 500 900 450 Number of Active Users Per Trunk 13 95 Network Analysis Corporation MALDeKI MEIDFORD APPROX SCALE I 2500 KEY MAP Figure D la 13 96 Network Anew Wm are A 1 1V w es - - A1 MAP 1 Figure D lb 13 17 TB 95 ISZ I04- MAP 2 Figure D lc 13 98 ■ I Network Analysis Corporation J96 O O 3o 200 72 if 182 i 164 168 A_ j 17© 162 HO 3 A 7© 176 200 154 96 fl_A54 7a t -bcr1 1 £_fl 74 dlS6 i S2 126 76 2J2 198 1 162 MAP 3 Figure D ld 13 99 I 156 10 92 ZiJU' 3 Network Analysis Corporation 'o tirst ' '• s ür the fieri iV rö trim ' i t •- c V 'v dt r ic ' ■« ■ i-v er 1 i-oio iö - o local tia jc « • i r c 15 active users fci nCO '•• ' «iO POL ' • '' I ■ H l V T 1 • i t v • cor ol M Ci'n'witrs conci ih jiovs muJ 1 iplo vOT p reV s u r i o anc sense opl•■•ui inn the design designs ' o do '' - ccT u j n - t irr ' V e are merely prr n ine MM i ' v i lc ra c nne i h v if-i 1 it • th« c f ■ ' • v devicor •n The Jos ' ••'■' - d-i » vi J L-v l nie 'a iJ »• ' 'v i od ly s u pj y indicating l h ■ location of the various devices on the map in tons oi an alphabetic label o i the map To ein j vi ni ' i ii« ' th ' design the number in the rectangle benido the l-ttcr en 1 he key maps point indicates the population downstream f vc that The designs ate as shown in Table D DFSICN % active terminals IS ' lotted Uns otted no ocvices no devices no devices converter at 10 v compressors 155 compressors at c'' and concentrators at b c at b Mb' a compressors at c'' and concentrators at h c i c' MC Table D 2 Feasible Designs for Central Transmission Mode Suppose now that X£ of the traffic from every terminal is local traffic whose destination is uniformly distributed throughout the network and suppose there are no routers compressors or concentrators converters Then every local Message must go from the originating terminal to the head end on reverse links and from the hea end to the destination terminal on reverse links Therefore each local inquiry traverses both forward and reverse 13 100 Network Analysis Corpomtön links instead of only reverse links as for central transmission Similarly each response occupies both forward and reverse links rather than only forward links as for central transmission The net effect is that for X% local traffic traffic in the branches is the same as if all the traffic were in the central transmission mode but the population were increased by X Hence the previous design procedures are still applicable and the design already given can be used fox local transmission superimposed on the central transmission provided the number of active users are appropriately adjusted 7or example the design for 10 - active terminals in the central transmission mode can be used for 8% active terminals with 25 of the traffic on a local basis In addition as an example if there were heavy traffic among the stations downstream of point d this might be handled by a iocal router at d 13 101 Network Analysis Corporation 15 APPENDIX E SPECIFICATIONS FOR FILTERS AND DATA AUGMEKTATIQN DEVICES BAND SEPARATION FILTERS The moct common two-way CATV configuration at present is the simplest single-trunk subchannel split in Figure El A much more sophisticated and flexible system is the dual trunk feederbacker arrangement in Figure E2 which is the system used in Boston For both these systems we must have an inexpensive simple method of interfacing with a converter or router to be added after the construction of the CATV system has been completed Furthermore the interface must be readily adaptable to other possible two-way configurations DMKTIOML COUHt« 54-260 'CEDE MKU 5-30 MTV THUHK MPllFlCft 0KtCT OM»L COUPLE« 154-260 41 JMHZ Figure El I Simplest two-way configuration 13 102 Network Analysis Corpon v 'tnmmm uNum ls-30 MHZ -omtcnoMi couru rau«» 54-260 MHZ motuMMM 5-30 MHZ 5-108 Figure E2 5-108 MHZ MHZL_ RCTVIM TRUM «MTLinCH Tiowu count Feederbacker Configuration The problem is readily solved by use of a pair of diplex filters as shown in Figure E3 or in some cases by a pair of triplex filters as shown in Figure E4 The units can be housed in casings a few inches in each dimension and are readily installed on line The passbands of the filters can be set for the particular system transmission frequencies The conditions for perfect band separation are that the passbands of the filter Ff F and F do not overlap and that the passbands cover uiie full frequency range of the channel Thus for the two-way configuration in Figure 4 1 the triplex filter is used with the following passbands F passes the signals at carrier frequencies wf and CO F passes the signals at carrier frequencies co and «' F passer all frequencies not passed by Ff and F Ff therefore isolates the forward channel for conversion or routing and F the reverse channel For the feederbacker configuration in Figure E 2 the diplex filter is used for line A with F_ and F specified as follows Ff passes the signals at carrier frequencies wf and w' f F passes all frequencies not passed by Ff 13 103 Network Analysis Corporation diplex filter Figure E3 to converter or router Diplex Band Separation Filter to converter or router triplex filter Figure E4 diplex filter triplex filter to converter or router Triplex Band Separation Filter 13 104 Network Analysis Corporation For standard CATV circuits each band separation unit adds a flat insertion loss of at most 1 75 db To make up this loss the gain of the subsequent amplifier might be increased by 3 5 db With most lines of equipment this simply means reducing the value of the input attenuation pad by 3 5 db However if the attenuator is already set at too low a value then the 3 5 db can be made up by increasing the size of the cable feeding into the band separation filter For example for a broad range of foam dielectric coaxial cables ehe difference between the losses of 5 inch and 75 inch coaxial cable at channel 13 is about 4 db 100 ft Thus less than 900 feet of cable would have to be converted from 5 inch to 75 inch This change would necessitate that at nest ten subscriber taps be changed in value and that the equalizer for one amplifier be adjusted—all minor adjustments to an existing system The required specifications for the individual filters are consistent with typical parameters for CATV bandpass and notch filters For example the characteristics below are more than adequate for the data system and are derived from off-the-shelf CATV filters Jerrold Filter Specifications FILTER SPECIFICATIONS Center Frequency Bandwidth Insertion Loss Impedance Passband Group Delay Variation Passband Ripple Stopband Attenuation in the range 30-260 MHZ 5 5 MHZ at 5 db points 1 25 at low VHF to 1 75 at high VHF 75 fi -23 db reflection coefficient 10 nanoseconds max 01 db max at least 30 db at 5 db bandedga plus 1 MHZ Table E1 - 3 105 r Network Analysis Corporation CONVERTERS The converter specifications are in Table E2 function input impedence output impedence convert carrier frequencies in VHF range 75Q -23 db reflection coefficient 75Ö -23 db reflection coefficient oscillator accuracy conversion gain noise figure 005% 5 db min 10 db in analog mode 75 db over 6MHZ Bandwidth amplitude variation Table E2 COMPRESSORS CONCENTRATORS AND ROUTERS The compressors concentrators and routers all operate digitally at the same frequencies and data rates and differ only in details and relative memory and logic requirements The specifications for all three are given in Table E3 Compressor number of inputs number of outputs input data rate output data rate throughput packets packet length carrier frequency core memory requirement Concentrator 3 3 3 3 100KB sec 100KB sec 1 Megabit sec 1 Megabit sec 1 packet 11 5 msec 1 packet 11 5msec 1150 bits packet 1150 bits packet Router 3 3 100KB sec or 1 Megabit sec 100KB sec or 1 Megabit sec 1 packet 11 5msec for 100 Kbit operation 1150 bits packet VHF range VHF range VHF range two packers six packets two packets Table E3 13 106 Network Analysis Corporation 14 References 1 Abramson N Excess Capacity of a Slotted Aloha System Privately circulated memorandum 1972 a 2 Abramson N Packet-Switching with Satellites National Computer' Conference June 1973 pp 695-702 3 Abramson N The ALOHA System—Another Alternative for Computer Communications AFIPS Conference Proceedings Vol 37 November 1970 pp 281-285 4 Abramson N The Aloha System Computer-Communication Networks N Abramson and F Kus edsj Prentice Hall N Y 1973 5 Abramson N The Spatial Capacity of an ALOHA Channel PRTN 49 April 30 1973 6 Baran P Tb Multiplexing Station Rand Corporation Memorandum RM-3578-PR August 1964 7 Bell Telephone Laboratories Transmission Systems for Communications 1971 8 Boehm S P P Baran Digical Simulation of Hot-Potato Routing in a Broadband Distribution Communications Network Rand Corporation Memorandum RM-3103-PR Aug 1964 9 Bouknight W J and G R Grussman DiM Grothe The ARPA Network Terminal System A New Approach to Network Access Datacomm 1973 10 Collins Radio Propagation Considerations and Po- er Budget Network Information Center Stanford Research Institute 1974 11 Chou W and H Frank Routing Strategies for Computer Network Design B P I Symposium 1972 12 Cuccia C L Phase Shift Keying The Optimum Modulation Technique for DIGICOM Microwave Systems News Vol 3 No 14 January 1973 p 3 14 1 Network Analysis Corporation 13 Floyd R Treesort Algoritnm 1x3 ACM Collected AIgurittms August IS02 14 Fralick S Performance of Some Spread Spectrum Modes PÄiiV 59 Jane 1 1 73 a lb Fralick S Tnrougnput for Time Capture Spread Spectrum PRTti 43 April lb 1973 lb Frank b and W Cnou Topologicai Design of Computer Networks ' Proceeahuj of IEEE 1973 17 Frank h I T Friscn and W Chou Topologicai Considerations in the Design of the ARPA Computer Network Proceedings of Spring Joint Computer Conference 1970 18 Frank H R Kahn L Kleinrock Computer Communication Network Design Experience with Theory and Practice Spring Joir ' Computer Conference April 1972 19 Frank h and R VanSlyke Reliability Considerations in the Growth of Computer Communications Networks Proceedings of 1973 NIC Conference November 1973 20 Fratta L M Gerla and L Kleinrock The Flow Deviation Method An Approach to Store-and-Forward Communication Network Design Networks 3 97-133 1973 21 Friedlander G D Super Communications For World Traders IEEE Spectrum March 1972 pp 74-83 22 Fuchs E and P E Jackson Estimates of Distributions of Random Variables for Certain Computer Communications Traffic Models Communications of the ACM Vol 13 N12 Dec 1970 pp 752-757 23 Garfinkel Robert S G L Nemhouser Wiley 1972 24 Gerla M Deterministic and Adaptive Routing Policies in Packet-Switched Computer Networks Proceedings of 3rd Data Communications Symposium of ACM Tampa Fla Nov 1973 25 Gerla M The Design of Store-and-Forward Networks for Computer Communications School of Engineering and Applied Science university of California Los Angeles PhD Dissertation January 1973 14 2 Integer Programming Network Analysis Corporation 26 Graham R L and H O Pollack On the Addressing Problem for Loop Switching BSTJ Vol 50 No 8 October 1971 27 Heart F E R E Kahn S N Ornstein W R Crowther and D C Waiden The Interface Message Processor For the ARPA Computer Network Spring Joint Computer Conference May 1970 pp 551-567 28 Hu l C Integer Programming and Network Flows Addison-Wesley Reading Mass 1969 29 Jackson P E and CD Stubbs A study of Multi-access Computer Communications Proceedings AFIPS 1969 Spring Joint Computer Conference Vol 34 AFIPS Press Montvale New Jersey pp 491-504 30 Jerrold Electronics Single VHF-Channel Pass-Band Filters Technical Data Sheet CS-TDS-7047 31 Jerrold Electronics Corporation 1971 National Cable Television Convention Publicity Release on Two-Way CATV Systems 32 Kahn R E Packet Radio Issues Network Information Center Stanford Research Institute 1974 33 Kaiser R L Spread-Spectrum Considerations Private Communication January 22 1973 34 Kershenbaum A and R VanSlyke Computing Minimum Spanning Trees Efficiently Proceedings of 1972 ACM Conference Boston August 1972 pp 518-527 35 Kleinrock L S S Lam Analytical Results for the ARPANET Satellite System Model Including the Effects of the Retransmission Delay Distribution 455 Vote 12 Network Information Center August 22 1972 36 Kleinrock L S S Lam On SLdDility of Packet-Switching in a Random Multi-access Broadcast Channel Seventh Hawaii International Conference on System Sciences Jan 1974 37 Kleinrock L S S Lam Packet-Switching in a Slotted Satellite Channel National Computer Conference June 1973 pp 703-710 38 Kruskal J B Jr On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem Proceedings of American Mathematical Society 7 1956 pp 4 8-50 39 LaRosa R Switchable and Fixed-Code Surface Wave Matched Filters Proceedings of the 1972 Symposium on Spread Spectrum Communications Naval Electronics Laboratory Center San Diego California 14 3 Network Analysis Corporation 40 Lawler E L The Complexity of Combinatorial Computations A Survey Pvooe eain js of Symposium on Computers and Automata Polytechnic Institute of Brooklyn April 1971 41 Ltung J ALOHA System with Caputre in a Multipath Environment PRTN 25 March 22 1973 42 Matthaei G L Acoustic Surface-Wave Transversal Filters IEEE Transactions on Circuit Theory Vol CT-20 No 5 September 1973 pp 459-470 43 McGuire R J Processing Spread Spectrum Signals PRTN 33 March 26 197 44 Mertz P Influence of Echoes on TV Transmission Journal of the SMPTE May 1953 45 Miller R E and J W Thatcher eds Complexity of Computer Computations Plenum 1972 46 Network Analysis Corporation NAC A Simulation of the Packet Radio Network Network Information Center Stanford Research Institute 1974 in preparation 47 NAC Directed versus Shared Channels for the Packet Radio Network Network Information Center Stanford Research Institute 1974 in preparation 48 NAC Implementation of Packet Radio Routing Algorithms Network Information Center Stanford Research Institute 1974 in preparation 49 NAC Location of Transponders for Area Coverage 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Network Information Center Stanford Research Institute Menlo Park California 57 Roberts L G Extensions of Packet Communication Technology to a Hand Held Personal Terminal Spring Joint Computer Conference Atlantic City May 16 1972 pp 295-303 a 58 Roberts L G Personnel Communication 1972 b 59 Roberts L G and B D Wessler The ARPA Network ComputerCommunication Networks N Abramson and F Kuo edd Prentice Hall 1973 ou Kogeness G Contributing Sources and Magnitudes of Envelope Delay in Cable Transmission System Components Official Transcript 21st Annual National Cable Television association Convention Chicago May 14-17 1972 61 Roth R H Computer Solutions to Minimum Cover Problems ORSA 17 pp 455-466 62 Schwartz M W R Bennett and S Stein Communication Systems and Techniques McGraw-Hill 19 66 63 Sloan Commi -' The Teh 64 SRI Measurement and Propagation NIC 1974 a Network Information Center Stanford Research Institute 65 SRI RF Capacity Considerations ibid 1974 b 66 SRI Spread Spectrum Ibid 1974 c 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