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

Hau L. Lee · Morris A. Cohen

86 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

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.

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References

1978Approximations for the M/G/m Queue 1983The convexity of the mean queue size of the M/M/c queue with respect to the traffic intensity

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