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Monotonicity results for MR/GI/1 queues

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Nicole Bäuerle
Nicole Bäuerle*
Affiliation:
University of Ulm
*
∗Postal address: Department of Mathematics VII, University of Ulm, D-89069 Ulm, Germany.
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Abstract

This paper considers queues with a Markov renewal arrival process and a particular transition matrix for the underlying Markov chain. We study the effect that the transition matrix has on the waiting time of the nth customer as well as on the stationary waiting time. The main theorem generalizes results of Szekli et al. (1994a) and partly confirms their conjecture. In this context we show the importance of a new stochastic ordering concept.

Keywords

MARKOV RENEWAL QUEUESSUPERMODULAR FUNCTIONSSTOCHASTIC ORDERING

MSC classification

Primary: 60K25: Queueing theory
Type
Research Article
Information
Journal of Applied Probability , Volume 34 , Issue 2 , June 1997 , pp. 514 - 524
Copyright
Copyright © Applied Probability Trust 1997 

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