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The stability of infinite-server networks with random routing

Published online by Cambridge University Press:  14 July 2016

S. A. Berezner  and
V. A. Malyshev
S. A. Berezner
Affiliation:
Moscow State University
V. A. Malyshev*
Affiliation:
Moscow State University
*
∗ Postal address for both authors: Probability Chair, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, USSR.
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Abstract

We consider networks with a very large or infinite number of nodes, linked by cable channels. The request which comes to a node is ordered to occupy a certain route of successive channels. The functioning of the system is regulated by the reserving of channels in order of the arrivals of the requests. Under some general conditions the existence of an ergodic region for such networks is proved. The practical value of the result lies in the fact that these conditions do not depend on the size of the graph.

Keywords

CHANNEL-SWITCHING NETWORKSGENERALIZED FIFO PROTOCOLWAITING TIME PROCESSLIMITING STATIONARY PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 2 , June 1989 , pp. 363 - 371
Copyright
Copyright © Applied Probability Trust 1989 

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References

[1] Borovkov, A. A. (1972) Stochastic Processes in Queueing Theory. Nauka, Moscow.Google Scholar
[2] Franken, P., König, D., Arndt, V. and Schmidt, V. (1981) Queues and Point Processes. Akademie-Verlag, Berlin.Google Scholar
[3] Kelbert, M. Y. and Sukhov, Y. M. (1985) Weak dependence of random field, describing the state of network at low transient streams (in Russian). Probl. Pered. Inf. 21, 89–98.Google Scholar
[4] Kelly, F. P. (1986) Blocking probabilities in large circuit-switched networks. Adv. Appl. Prob. 18, 473–505.CrossRefGoogle Scholar
[5] Malyshev, V. A. and Ignatyuk, I. A. (1987) Locally interacting processes with noncompact set of values (in Russian). Vest. Mosk. Univ. (Ser. Math.) N2, 3–6.Google Scholar
[6] Mikhaylov, V. A. and Rybko, A. N. (1986) Ergodicity region of channel-switching networks (in Russian). Probl. Pered. Inf. 22, 66–84.Google Scholar