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Insensitive average residence times in generalized semi-Markov processes

Published online by Cambridge University Press:  01 July 2016

A. D. Barbour  and
R. Schassberger
A. D. Barbour*
Affiliation:
Gonville and Caius College, Cambridge
R. Schassberger*
Affiliation:
Technical University of Berlin
*
∗Postal address: Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, U.K.
∗∗Postal address: Fachbereich Mathematik, Technische Universität Berlin, Strasse des 17. Juni 135, D-1000 Berlin 12, Germany.
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Abstract

For a broad class of stochastic processes, the generalized semi-Markov processes, conditions are known which imply that the steady state distribution of the process, when it exists, depends only on the means, and not the exact shapes, of certain lifetime distributions entering the definition of the process. It is shown in the present paper that this insensitivity extends to certain average and conditional average residence times. Particularly interesting applications can be found in the field of networks of queues.

Keywords

GENERALIZED SEMI-MARKOV PROCESSESINSENSITIVITYNETWORKS OF QUEUES
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 4 , December 1981 , pp. 720 - 735
Copyright
Copyright © Applied Probability Trust 1981 

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