processing, intersymbol interference, data compression, and cryptog- Dr. Hellman is a member of Tau Beta Pi and Eta KappaNU. He raphy. He has consulted in the areas of communications, informa is President of theSan Francisco Section’s IEEE Information tion theory, and general engineering forvarious industries and Theory Group’s Chapter, and was Publications Chairman for the laboratories. He is the liaison at Stanford for its Industrial Aaliates 1972 Information Theory Symposium. He is an Associate Editor Program in Information Systems, a program designed to increase for Communication Theory of the IEEE TRANSACTIONSON COM- interaction between industry and the university. MUNICATIONS. Packet Switching in a Multiaccess Broadcast Channel: Performance Evaluation Abstract-In this paper, the rationale and some advantages for and methods for the evaluation and optimization of the multiaccessbroadcast packet communication usingsatellite and channelperformance of a slotted ALOHA system. The ground radio channels arediscussed. A mathematical model is form- ulated for a “slotted ALOHA” random access system. Using this problem of performance evaluation is addressed in this model, a theory is put forth which gives a coherent qualitative inter- paper. In [l], we present dynamic channel control pro- pretation of the system stability behavior which leads to the defini- cedures as solutions to some of the issues considered herein. tion of a stability measure. Quantitative estimates for the relative In this paper, the rationale for multiaccess broadcast instability of unstable channels are obtained. Numerical results are packet communication is first discussed. The mathematical shown illustratingthe trading relationsamong channel stability, throughput, and delay. These results provide tools for the perform- model to be considered is then described. Following that, a ance evaluation and design of an uncontrolled slotted ALOHA sys- theory is proposed which explains the dynamic and tem. Adaptive channel control schemes are studied in a companion stochastic channel behavior. In particular, we display the paper. delay-throughput performance curves obtained under the assumption of equilibrium conditions [6]. We then demon- INTRODUCTION strate that a slotted ALOHA channel often exhibits “un- N THIS and a forthcoming paper [l], a packet switch- stable behavior.” A stability definition is proposed which I ing technique based upon the randomaccess concept of characterizesstable and unstable channels. Astability the ALOHA System [Z] will be studied in detail. This measure (FET) is then defined which quantifies the technique, referred to as slotted ALOHA random access, relative instability of unstable channels. An algorithm is enables efficient sharing of a data communicatiori channel given for the calculation of FET. Finally, numerical results by a large population of users, each with a bursty data are shown which illustrate the trading relations among stream. This packet switching technique may be, applied channel stability, channel throughput, and average packet tothe use of satelliteand groundradio channels for delay. Our main concern in this paper is the consideration computer-computer and terminal-computer communica- of the stabilityissue and its effecton the channel through- tions, respectively’ [3]-[10]. The multiaccess broadcast put-delay performance. capabilities of these channels render them attractive solu- tions to two problems: 1) large computer-communication MULTIACCESS BROADCAST PACKET networkswith nodes distributed over wide geographic COMMUNICATION areas,and 2) largeterminal access networkswith po- Rationale tentially mobile terminals. The objective of this studyis to develop analytic models For almost a century, circuit switching dominated the design of communication networks. Only with the higher Paper approved bythe Associate Editor for Computer Com- speed and lower cost of modern computers did packetcom- munication of the IEEE CommunicationsSociety for publication munication become competitive. It was not until approxi- after presentation at the 7th Hawaii International Conference on System Sciences, Honolulu, Hawaii, January 8-10, 1974. Manuscript mately 1970 that the computer (switching) cost dropped received June 30, 1974; revised September 30, 1974. This research below the communication (bandwidth) cost in a packet was supported by the Advanced Research Projects Agency of the Department of Defense under Contract DAHC 15-73-C-0368. switching network [ll]. This also marked the first ap- L. Kleinrockis withthe Department of Computer Science, pearance of packet switched computer-communication University of California, Los Angeles, Calif. 90024. S. S. Lam is with the IBM Thomas J. Watson Research Center, networks [Z], [12]. Yorktown Heights, N. Y. 10598. Circuit switching is relatively inefficient for computer XLEINROCK AND LAM: PACKET SWITCHING 41 1 communications, especially over long distances. Measure- stations covered by the transponder beam. Thus, a satel- mentstudies [13] conducted on time-sharing systems lite channel (consisting of both carrier frequencies) pro- indicate that bothcomputer and terminal datastreams are vides a completely connected network topology for all bursty. Depending on the channel speed, the ratiobetween earth stations covered by the transponderbeam. the peak andthe average datarates may be as high: Consider the use of packet communication in a com- as 2000 to 1 [SI. Consequently, if a high-speed point-to- puter-communication networkenvironment tosupport point channel is used, the channel utilization may be ex- large populatons of (bursty) users over a wide area. We tremely low since the channel is idle most of the time. On can then identify and summarize the following advantages the other hand, if a low-speed channel is used, the trans- of satellite and ground radio channels over conventional mission delay is large. wire communications. The above dilemma is caused by channel users imposing 1) Elimi?lation of ComplexTopological Design and bursty random demandson their communication channels. RoutingProblems: Topological design and routing prob- By the law of large numbers in probability theory, the lems are verycomplex in networks with a large population total demand at any instant from a large population of of users. Existing implementations suitable for a (say) 50 independentusers is, with high probability, approxi- node network may become totally inappropriate for a 500 mately equal to the sum of their average demands (i.e., a node network required to perform thesame functions nearlydeterministic quantity).Thus, if a channel is [21]. On theother hand, ground radio andsatellite dynamically shared in some fashion among many users, channels used in themultiaccess broadcast mode provide a the required channel bandwidth to satisfy a given delay completely connected network topology, since every user constraint may be much less than if the users are given may access any other user covered by the broadcast. dedicated channels. This concept is known as statistical load 2) Wide Geographical Areas: Wire communications be- averaging and has been applied in many computer-com- come expensive over long distances (e.g., transcontinental, munication schemes to various degrees of success. These transoceanic). Even on a local level, the communication schemes include: polling systems [14], loop systems [15], cost, for an interactive user on an alphanumeric console asynchronous time division multiplexing (ATDM) [lS], over distances of over 100 miles may easily exceed the cost andthe store-and-forward packet switching concepts of computation [2]. On the other hand, satellite andradio [17]-[19] implemented in the ARPA network [lz]. communications are relatively distance independent, and We are currently facing an enormous growth in com- are especially suitable for geographically scattered users. puter networks [20]. To design cost-effective computer- 3) Mobility of Users: Since radio is a multiaccess broad- communication networks for the future, new techniques cast medium, it is possible for users to move around freely. are needed which are capable of providing efficient high- This consideration willsoon become importantin the speed computer-computer and terminal-computer com- development of personal terminals in future telecommuni- munications in a large network environment. The applica- cation systems [22] as well as in aeronautical and mari- tion of packet switching techniques to radio communica- time applications [23]. ti.on (both satellite andground radio channels) appears to 4) LargePopulation of Activeand Inactive Users: In provide a solution. wire communications, the system overhead usually in- Radio is a multiaccess broadcast medium. That is, a creases with the number of users (e.g., polling schemes). signal generated by a radio transmitter may be received The maximum number of users is often bounded by some over a wide area by any number of receivers. This is hardware limitation (e.g., the fan-in of a communications referred to as the broadcast capability. Furthermore, any processor). In radio communication, since each user is number of users maytransmit signals over the same merely represented by an ID number, the number of channel. This is referred to as the multiaccess capability. active users is bounded only by the channel capacity and (However, if two signals at the same carrier frequency thereis no limitation tothe number of inactive (but overlap intime at a radio receiver', we assume that potentially