Journal of Applied Probability: Volume 20 - Issue 4

Conditional response times in the M/G/1 processor-sharing system
B. K. Asare, F. G. Foster
Published online by Cambridge University Press:

14 July 2016, pp. 910-915
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The expected response time of a job that requires processing time t and meets n jobs on arrival in the M/G/1 processor-sharing system is derived.

The convexity of the mean queue size of the M/M/c queue with respect to the traffic intensity
W. Grassmann
Published online by Cambridge University Press:

14 July 2016, pp. 916-919
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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.

A note on the convexity of performance measures of M/M/c queueing systems
Hau Leung Lee, Morris A. Cohen
Published online by Cambridge University Press:

14 July 2016, pp. 920-923
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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.

Journal of Applied Probability