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Perturbation theory approach for a class of hybrid switching networks with small transit flows

Published online by Cambridge University Press:  01 July 2016

M. Ya. Kelbert ,
R. P. Kopeika ,
R. N. Shamsiev  and
Yu. M. Sukhov
M. Ya. Kelbert*
Affiliation:
Institute for Problems of Information Transmission
R. P. Kopeika*
Affiliation:
Institute for Problems of Information Transmission
R. N. Shamsiev*
Affiliation:
Institute for Problems of Information Transmission
Yu. M. Sukhov*
Affiliation:
Institute for Problems of Information Transmission
*
Postal address for all authors: Institute for Problems of Information Transmission, USSR Academy of Sciences, GSP-4 Moscow 101447, USSR.
Postal address for all authors: Institute for Problems of Information Transmission, USSR Academy of Sciences, GSP-4 Moscow 101447, USSR.
Postal address for all authors: Institute for Problems of Information Transmission, USSR Academy of Sciences, GSP-4 Moscow 101447, USSR.
∗Research partly carried out at BiBoS Research Centre, University of Bielefeld, D-4800 Bielefeld, FRG.
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Abstract

A method originating from statistical mechanics (low-density and high-temperature expansions) is used to prove the existence and uniqueness of a stationary regime for switching networks on finite or infinite graphs. The main assumption is that the message (customer) flows circulating through the network are ‘localized' in the sense that, for any message, the probability of having a long path is rapidly decreasing (and, moreover, a path of a ‘typical' message consists of one line). The switching rule combines message-switching and circuit-switching principles. The stationary regime for the network under consideration may be treated as a ‘small perturbation' of the ‘idealized' regime in the totally decoupled network where all the messages have single line paths.

Keywords

STATIONARY REGIMEFAMILY OF MARKED POINT PROCESSESSOLUTION TO A SYSTEM OF STOCHASTIC EQUATIONSEXISTENCE AND UNIQUENESSMAJORIZATION PROPERTIESWEAK DEPENDENCE
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 1 , March 1990 , pp. 211 - 229
Copyright
Copyright © Applied Probability Trust 1990 

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References

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