International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1992 / Article

Open Access

Volume 5 |Article ID 843287 | https://doi.org/10.1155/S1048953392000273

A. Mehrez, J. Brimberg, "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", International Journal of Stochastic Analysis, vol. 5, Article ID 843287, 5 pages, 1992. https://doi.org/10.1155/S1048953392000273

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

Received01 Dec 1992

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.

Copyright © 1992 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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