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A Convexity Property of a Markov-Modulated Queueing Loss System

Published online by Cambridge University Press:  27 July 2009

Charles Du  and
Michael Pinedo
Michael Pinedo
Affiliation:
Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
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Abstract

In this note we consider a single-server queueing loss system with zero buffer. The arrival process is a nonstationary Markov-modulated Poisson process. The arrival process in state i is Poisson with rate λi. The process remains in state i for a time that is exponentially distributed with rate Cαi, with c being a control or speed parameter. The service rate in state i is exponentially distributed with rate μi. The process moves from state i to state j with transition probability qij. We are interested in the loss probability as a function of c. In this note we show that, under certain conditions, the loss probability decreases when the c increases. As such, this result generalizes a result obtained earlier by Fond and Ross.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 2 , April 1995 , pp. 193 - 199
Copyright
Copyright © Cambridge University Press 1995

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