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Lookup NU author(s): Emeritus Professor Isi Mitrani
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An M/M/N queue, where each of the processors is subject to independent random breakdowns and repairs, is analyzed in the steady state under two limiting regimes. The first is the usual heavy traffic limit where the offered load approaches the available processing capacity. The (suitably normalized) queue size is shown to be asymptotically exponentially distributed and independent of the number of operative processors. The second limiting regime involves increasing the average lengths of the operative and inoperative periods, while keeping their ratio constant. Again the asymptotic distribution of an appropriately normalized queue size is determined. This time it turns out to have a rational Laplace transform with simple poles. In both cases, the relevant parameters are easily computable.
Author(s): Mitrani I, Puhalskii A
Publication type: Article
Publication status: Published
Journal: Queueing Systems - Theory and Applications
ISSN (print): 0257-0130
ISSN (electronic): 1572-9443
Publisher: Springer New York LLC
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