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The sojourn time distribution in an infinite server resequencing queue with dependent interarrival and service times

Published online by Cambridge University Press:  14 July 2016

Tijs Huisman*
Affiliation:
University of Amsterdam
Richard J. Boucherie*
Affiliation:
University of Amsterdam
*
Current address: Railned BV, Department of Innovation, PO Box 2101, 3500 GC Utrecht, The Netherlands. Email address: t.huisman@railned.nl
∗∗ Current address: Stochastic Operations Research Group, Faculty of Mathematical Sciences, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands.

Abstract

We consider an infinite server resequencing queue, where arrivals are generated by jumps of a semi-Markov process and service times depend on the jumps of this process. The stationary distribution of the sojourn time, conditioned on the state of the semi-Markov process, is obtained both for the case of hyperexponential service times and for the case of a Markovian arrival process. For the general model, an accurate approximation is derived based on a discretisation of interarrival and service times.

MSC classification

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2002 

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