Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-07-02T06:51:34.970Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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