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A Simple Proof of Instability of a Random-Access Communication Channel

Published online by Cambridge University Press:  27 July 2009

Sheldon M. Ross
Affiliation:
Department of Industrial Engineering and Operations Research University of California, Berkeley, California 94720

Abstract

We give an extremely simple argument to prove that in infinite user-commurlication channels, under the Aloha protocol, the number of successful transmissions is finite with probability 1. The same result is then shown to hold for those back-off protocols whose transmission probabilities are bounded away from 0.

Type
Articles
Copyright
Copyright © Cambridge University Press 1988

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References

Referenecs

Aldous, D.J. (1987). Ultimate instability of exponential back-off protocol for acknowledgment-based transmission control of random-access communication channels. IEEE Transactions Information Theory IT-33(2): 219223.CrossRefGoogle Scholar
Fayolle, G. & Iasnogorolski, R. (1987). Criteria for nonergodicity of stochastic processes. Journal of Applied Probability 24(2): 347354.CrossRefGoogle Scholar
Kaplan, M. (1979). A sufficient condition for nonergodicity of a Markov chain. IEEE Transactions Information Theory 25: 470471.CrossRefGoogle Scholar
Rosenkrantz, W. & Towsley, D. (1983). On the instability of slotted Aloha multiaccess algorithm. IEEE Transactions on Automatic Control 28: 994996.CrossRefGoogle Scholar
Sennaott, L. (1987). Conditions for the nonergodicity of Markov chains with application to a communication system. Journal of Applied Probability 44: 339346.CrossRefGoogle Scholar