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A Markov chain approach to periodic queues

Published online by Cambridge University Press:  14 July 2016

Søren Asmussen  and
Hermann Thorisson
Søren Asmussen
Affiliation:
University of Copenhagen
Hermann Thorisson*
Affiliation:
University of Göteborg
*
∗∗Postal address: Department of Mathematics, Chalmers University of Technology and University of Göteborg, S-41296 Göteborg, Sweden.
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Abstract

We consider GI/G/1 queues in an environment which is periodic in the sense that the service time of the nth customer and the next interarrival time depend on the phase θ n at the arrival instant. Assuming Harris ergodicity of {θ n} and a suitable condition on the traffic intensity, various Markov chains related to the queue are then again Harris ergodic and provide limit results for the standard customer- and time-dependent processes such as waiting times and queue lengths. As part of the analysis, a result of Nummelin (1979) concerning Lindley processes on a Markov chain is reconsidered.

Keywords

PERIODICITYQUEUEHARRIS RECURRENCELINDLEY PROCESSWAITING TIMEQUEUE LENGTHCOUPLING
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 215 - 225
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

∗

Present address: Institute of Electronical Systems, Aalborg University, Strandvejen, DK-9000 Aalborg, Denmark.

Supported by the Swedish Natural Science Research Council and by the Icelandic Science Foundation.

References

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