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The convexity of the mean queue size of the M/M/c queue with respect to the traffic intensity

Published online by Cambridge University Press:  14 July 2016

W. Grassmann
W. Grassmann*
Affiliation:
University of Saskatchewan
*
∗ Postal address: Department of Computational Science. University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 0W0.
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Abstract

In this paper, we show that the expected number in an M/M/c queue is convex with respect to the traffic intensity. The proof is conducted by expressing the second derivative of the expected queue size as the sum of non-negative terms.

Keywords

MULTISERVER QUEUEVARYING ARRIVAL RATES
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 4 , December 1983 , pp. 916 - 919
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

Research partly carried out while the author was a Visiting Scholar in the Department of Operations Research at Stanford University.

References

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