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Limiting Results for Multiprocessor Systems with Breakdowns and Repairs

Lookup NU author(s): Emeritus Professor Isi Mitrani

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Abstract

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.

Publication metadata

Author(s): Mitrani I, Puhalskii A

Publication type: Article

Publication status: Published

Journal: Queueing Systems - Theory and Applications

Year: 1993

Volume: 14

Issue: 3-4

Pages: 293-311

ISSN (print): 0257-0130

ISSN (electronic): 1572-9443

Publisher: Springer New York LLC

URL: http://dx.doi.org/10.1007/BF01158870

DOI: 10.1007/BF01158870

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