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A discrete-time queueing network

Published online by Cambridge University Press:  14 July 2016

Jean Walrand
Jean Walrand*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Electrical Engineering and Computer Sciences and the Electronics Research Laboratory, University of California, Berkeley, CA 94720, U.S.A.
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Abstract

A discrete-time network with multiple transitions is defined. It is characterized by the independence of the service processes at different nodes. That network is shown to have the familiar quasi-reversibility properties.

Keywords

REVERSIBILITYPRODUCT FORM
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 4 , December 1983 , pp. 903 - 909
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

This research was supported in part by the N.S.F. under Grant ECS-8205428.

References

[1] Daduna, H. and Schassberger, R. (1982) Networks of queues in discrete time. Preprint, Technische Universität Berlin.Google Scholar
[2] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
[3] Kobayashi, H. (1975) On discrete-time processes in a packetized communication system. ALOHA System Technical Report B75–28, University of Hawaii.Google Scholar
[4] Schassberger, R. (1981) The doubly stochastic server: A time-sharing model. Z. Operat. Res. 25, 179–189.Google Scholar
[5] Walrand, J. (1983) A probabilistic look at networks of queues. IEEE Trans. Information Theory IT-29 (6).Google Scholar
[6] Walrand, J. and Varaiya, P. (1980) Interconnections of Markov chains and quasi-reversible queuing networks. Stoch. Proc. Appl. 10, 209–219.Google Scholar