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TRAFFIC GENERATED BY A SEMI-MARKOV ADDITIVE PROCESS

Published online by Cambridge University Press:  02 November 2010

Joke Blom  and
Michel Mandjes
Joke Blom
Affiliation:
CWI 1098 XG Amsterdam, The Netherlands E-mail: joke.blom@cwi.nl
Michel Mandjes
Affiliation:
Korteweg-de Vries Institute for Mathematics, University of Amsterdam, 1098 XH Amsterdam, The Netherlands; Eurandom, Eindhoven, The Netherlands; CWI, Amsterdam, The Netherlands E-mail: m.r.h.mandjes@uva.nl
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Abstract

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We consider a semi-Markov additive process A(·)—that is, a Markov additive process for which the sojourn times in the various states have general (rather than exponential) distributions. Letting the Lévy processes Xi(·), which describe the evolution of A(·) while the background process is in state i, be increasing, it is shown how double transforms of the type $\vint_{0}^{\infty} e^{-qt}\, {\open E} \lsqb e^{-\alpha A(t)}\, {d}t \rsqb$ can be computed. It turns out that these follow, for given nonnegative α and q, from a system of linear equations, which has a unique positive solution. Several extensions are considered as well.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 1 , January 2011 , pp. 21 - 27
Copyright
Copyright © Cambridge University Press 2011

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