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A BAYESIAN APPROACH TO FIND RANDOM-TIME PROBABILITIES FROM EMBEDDED MARKOV CHAIN PROBABILITIES

Published online by Cambridge University Press:  22 October 2007

Winfried K. Grassmann  and
Javad Tavakoli
Winfried K. Grassmann
Affiliation:
Department of Computer ScienceUniversity of SaskatchewanSaskatoon, S7N 5C9Canada E-mail: grassman@cs.usask.ca
Javad Tavakoli
Affiliation:
Department of Mathematics, Statistics and PhysicsUniversity of British Columbia OkanaganKelowna, V1V 1V7Canada E-mail: javad.tavakoli@ubc.ca
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Abstract

The embedded Markov chain approach is widely used in queuing theory, in particular in M/G/1 and GI/M/c queues. In these cases, one has to relate the embedded equilibrium probablities to the corresponding random-time probabilities. The classical method to do this is based on Markov renewal theory, a rather complex approach, especially if the population is finite or if there is balking. In this article we present a much simpler method to derive the random-time probabilities from the embedded Markov chain probabilities. The method is based on conditional probability. Our approach might also be applicable in such situations.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 4 , October 2007 , pp. 551 - 556
Copyright
Copyright © Cambridge University Press 2007

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