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The convexity of a general performance measure for multiserver queues

Published online by Cambridge University Press:  14 July 2016

Arie Harel  and
Paul Zipkin
Arie Harel*
Affiliation:
Rutgers University
Paul Zipkin*
Affiliation:
Columbia University
*
∗Postal address: Graduate School of Management, Rutgers University, Newark, NJ 07102, USA.
∗∗Postal address: Graduate School of Business, Uris Hall, Columbia University, New York, NY 10027, USA.
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Abstract

This paper examines a general performance measure for queueing systems. This criterion reflects both the mean and the variance of sojourn times; the standard deviation is a special case. The measure plays a key role in certain production models, and it should be useful in a variety of other applications.

We focus here on convexity properties of an approximation of the measure for the M/G/c queue. For c ≧ 2 we show that this quantity is convex in the arrival rate. Assuming the service rate acts as a scale factor in the service-time distribution, the measure is convex in the service rate also.

Keywords

M/G/c QUEUESOJOURN TIME
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 725 - 736
Copyright
Copyright © Applied Probability Trust 1987 

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