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Conditions for the non-ergodicity of Markov chains with application to a communication system

Published online by Cambridge University Press:  14 July 2016

Linn I. Sennott
Linn I. Sennott*
Affiliation:
Illinois State University
*
∗Postal address: Department of Mathematics, Illinois State University, Normal, IL 61761, USA.
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Abstract

We obtain a sufficient condition for the transience of a Markov chain, and a sufficient condition for its null recurrence. These are applied to characterize the stability of a multiple-access communication system. Performance bounds for the system are also obtained.

Keywords

TRANSIENCENULL RECURRENCEMULTIPLE-ACCESS COMMUNICATIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 2 , June 1987 , pp. 339 - 346
Copyright
Copyright © Applied Probability Trust 1987 

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References

Fayolle, G., Gelenbe, E. and Labetoulle, J. (1977) Stability and optimal control of the packet switching broadcast channel. J. Assoc. Comput. Mach. 24, 375–386.Google Scholar
Foster, F. G. (1953) On stochastic matrices associated with certain queueing processes. Ann. Math. Statist. 24, 355–360.CrossRefGoogle Scholar
Kaplan, M. (1979) A sufficient condition for nonergodicity of a Markov chain. IEEE Trans. Inf. Theory 25, 470–471.Google Scholar
Mertens, J.-F., Samuel-Cahn, E. and Zamir, S. (1978) Necessary and sufficient conditions for recurrence and transience of Markov chains in terms of inequalities. J. Appl. Prob. 15, 848–851.CrossRefGoogle Scholar
Pakes, A. G. (1969) Some conditions for ergodicity and recurrence of Markov chains. Operat. Res. 17, 1058–1061.Google Scholar
Rosenkrantz, W. and Towsley, D. (1983) On the instability of slotted ALOHA multiaccess algorithm. IEEE Trans. Auto. Control 28, 994–996.Google Scholar
Sennott, L. Humblet, P. and Tweedie, R. (1983) Mean drifts and the non-ergodicity of Markov chains. Operat. Res. 31, 783–789.Google Scholar
Szpankowski, W. (1985) Some sufficient conditions for non-ergodicity of Markov chains. J. Appl. Prob. 22, 138–147.Google Scholar
Tweedie, R. (1975) Relations between ergodicity and mean drift for Markov chains. Austral. J. Statist 17, 96–106.Google Scholar