A note on the convexity of the expected queue length of the M / M / s queue with respect to the arrival rate: a third proof

A. Mehrez and J. Brimberg

International Journal of Stochastic Analysis, 1992, vol. 5, 1-5

Abstract:

The convexity of the expected number in an M / M / s queue with respect to the arrival rate (or traffic intensity) is well known. Grassmann [1] proves this result directly by making use of a bound on the probability that all servers are busy. Independently, Lee and Cohen [2] derive this result by showing that the Erlang delay formula is a convex function. In this note, we provide a third method of proof, which exploits the relationship between the Erlang delay formula and the Poisson probability distribution. Several interesting intermediate results are also obtained.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:843287

DOI: 10.1155/S1048953392000273

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