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

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Tijs Huisman  and
Richard J. Boucherie
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: [email protected]
∗∗ Current address: Stochastic Operations Research Group, Faculty of Mathematical Sciences, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands.
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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.

Keywords

Resequencing queuesojourn time distributionsemi-Markovian arrival process

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 590 - 603
Copyright
Copyright © Applied Probability Trust 2002 

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