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Stationary IPA estimates for non-smooth functions of the GI/G/1/infini workload

Abstract : We give stationary estimates for the derivative of the expectation of a non-smooth function of bounded variation f of the workload in a GI/G/1/ queue, with respect to a parameter influencing the distribution of the input process. For this, we use an idea of Konstantopoulos and Zazanis based on the Palm inversion formula, however avoiding a limiting argument by performing the level-croissant analysis there of globally, via Fubini's theorem. This method of proof allows to treat the case where the workload distribution has a mass at discontinuities of f and where the formula has to be modified. The case where the parameter is the speed of service or/and the time scale factor of the input process is also treated using the same approach.
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https://hal.inria.fr/inria-00076900
Contributor : Rapport de Recherche Inria <>
Submitted on : Monday, May 29, 2006 - 11:17:34 AM
Last modification on : Friday, May 25, 2018 - 12:02:05 PM
Long-term archiving on: : Monday, April 5, 2010 - 9:21:23 PM

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  • HAL Id : inria-00076900, version 1

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Pierre Brémaud, Jean-Marc Lasgouttes. Stationary IPA estimates for non-smooth functions of the GI/G/1/infini workload. [Research Report] RR-1677, INRIA. 1992. ⟨inria-00076900⟩

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