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Stationary IPA estimates for nonsmooth G/G/1/∞ functionals via palm inversion and level-crossing analysis

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Abstract

We give stationary estimates for the derivative of the expectation of a nonsmooth function of bounded variationf of the workload in a G/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 [1992] based on the Palm inversion formula, however avoiding a limiting argument by performing the level-crossing analysis thereof globally, via Fubini's theorem. This method of proof allows to treat the case where the workload distribution has a mass at discontinuities off and where the formula of Konstantopoulos and Zazanis [1992] 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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Authors and Affiliations

  1. Laboratoire des Signaux et Systèmes, CNRS-ESE, Plateau du Moulon, 91190, Gif-sur-Yvette, France

    Pierre Brémaud

  2. Domaine de Voluceau, INRIA, Rocquencourt, B.P. 105, 78153, Le Chesnay Cedex, France

    Jean-Marc Lasgouttes

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  1. Pierre Brémaud
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  2. Jean-Marc Lasgouttes
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Brémaud, P., Lasgouttes, JM. Stationary IPA estimates for nonsmooth G/G/1/∞ functionals via palm inversion and level-crossing analysis. Discrete Event Dyn Syst 3, 347–374 (1993). https://doi.org/10.1007/BF01439159

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  • DOI: https://doi.org/10.1007/BF01439159

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