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The basic equations for a supplemented GSMP and its applications to queues

Published online by Cambridge University Press:  14 July 2016

Masakiyo Miyazawa  and
Genji Yamazaki
Masakiyo Miyazawa*
Affiliation:
Science University of Tokyo
Genji Yamazaki*
Affiliation:
Tokyo Metropolitan Institute of Technology
*
∗ Postal address: Department of Information Sciences, Science University of Tokyo, Noda City, Chiba 278, Japan.
∗∗ Postal address: Tokyo Metropolitan Institute of Technology, 6–6 Asahigaoka, Hino-city, Tokyo 191, Japan.
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Abstract

A supplemented GSMP (generalized semi-Markov process) is a useful stochastic process for discussing fairly general queues including queueing networks. Although much work has been done on its insensitivity property, there are only a few papers on its general properties. This paper considers a supplemented GSMP in a general setting. Our main concern is with a system of Laplace–Stieltjes transforms of the steady state equations called the basic equations. The basic equations are derived directly under the stationary condition. It is shown that these basic equations with some other conditions characterize the stationary distribution. We mention how to get a solution to the basic equations when the solution is partially known or inferred. Their applications to queues are discussed.

Keywords

PALM DISTRIBUTIONPOINT PROCESSSTATIONARY DISTRIBUTIONGENERATOR OF MARKOV PROCESSBASIC EQUATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 3 , September 1988 , pp. 565 - 578
Copyright
Copyright © Applied Probability Trust 1988 

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