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A note on the convexity of performance measures of M/M/c queueing systems

Published online by Cambridge University Press:  14 July 2016

Hau Leung Lee  and
Morris A. Cohen
Hau Leung Lee*
Affiliation:
Stanford University
Morris A. Cohen*
Affiliation:
The Wharton School, University of Pennsylvania
*
∗ Postal address: Department of Industrial Engineering and Engineering Management, Stanford University, Stanford, CA 94305, U.S.A.
∗∗ Postal address: Department of Decision Sciences, The Wharton School, University of Pennsylvania, PA 19104, U.S.A.
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Abstract

Convexity of performance measures of queueing systems is important in solving control problems of multi-facility systems. This note proves that performance measures such as the expected waiting time, expected number in queue, and the Erlang delay formula are convex with respect to the arrival rate or the traffic intensity of the M/M/c queueing system.

Keywords

ERLANG DELAY FORMULAQUEUEING THEORYOPTIMIZATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 4 , December 1983 , pp. 920 - 923
Copyright
Copyright © Applied Probability Trust 1983 

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References

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