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A Quasi-Reversibility Approach to the Insensitivity of Generalized Semi-Markov Processes

Published online by Cambridge University Press:  27 July 2009

Panagiotis Konstantopoulos  and
Jean Walrand
Panagiotis Konstantopoulos
Affiliation:
Department of Electrical Engineering and Computer Sciences and Electronics Research LaboratoryUniversity of California Berkeley, California 94720
Jean Walrand
Affiliation:
Department of Electrical Engineering and Computer Sciences and Electronics Research LaboratoryUniversity of California Berkeley, California 94720
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Abstract

This paper is concerned with a certain property of the stationary distribution of a generalized semi-Markov process (GSMP) known as insensitivity. It is well-known that the so-called Matthes' conditions form a necessary and sufficient algebraic criterion for insensitivity. Most proofs of these conditions are basically algebraic. By interpreting a GSMP as a simple queueing network, we are able to show that Matthes' conditions are equivalent to the quasi-reversibility of the network, thus obtaining another simple proof of the sufficiency of these conditions. Furthermore, we apply our method to find a simple criterion for the insensitivity of GSMP's with generalized routing (in a sense that is introduced in the paper).

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 3 , July 1989 , pp. 405 - 415
Copyright
Copyright © Cambridge University Press 1989

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