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A monotonicity result for the workload in Markov-modulated queues

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Nicole Bäuerle  and
Tomasz Rolski
Nicole Bäuerle*
Affiliation:
University of Ulm
Tomasz Rolski*
Affiliation:
University of Wroclaw
*
∗Postal address: Department of Mathematics VII, University of Ulm, D-89069 Ulm, Germany. Email address: [email protected].
∗∗Postal address: Mathematical Institute, University of Wroclaw, 50384 Wroclaw, Poland.
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Abstract

We consider a single server queue where the arrival process is a Markov-modulated Poisson process and service times are independent and identically distributed and independent from arrivals. The underlying intensity process is assumed ergodic with generator cQ, c > 0. We prove under some monotonicity assumptions on Q that the stationary workload W(c) is decreasing in c with respect to the increasing convex ordering.

Keywords

Markov-modulated queuestationary workloadincreasing convex orderingsupermodular function

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998 , pp. 741 - 747
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

Work supported in part by KBN under grant 2 PO3A 04608(1995–97).

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