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A monotonicity result for a single-server queue subject to a Markov-modulated Poisson process

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Qing Du
Qing Du*
Affiliation:
Columbia University
*
∗Postal address: Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA.
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Abstract

Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i = 1, 2, 3) is exponentially distributed with rate cα i. The arrival rate at level i is λ i and the service time is exponentially distributed with rate μ i. In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.

Keywords

POISSON ARRIVALS PROCESSZERO BUFFER

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 1103 - 1111
Copyright
Copyright © Applied Probability Trust 1995 

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