Stationary IPA Estimates for Non-Smooth G/G/1/∞ Functionals via Palm Inversion and Level-Crossing Analysis.

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 G/G/1/∞ queue, with respect to a parameter influencing the distribu- tion 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-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 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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Pierre Bremaud, Jean-Marc Lasgouttes. Stationary IPA Estimates for Non-Smooth G/G/1/∞ Functionals via Palm Inversion and Level-Crossing Analysis.. Discrete Event Dynamic Systems, Springer Verlag, 1993, 3 (4), pp.347-374. ⟨10.1007/BF01439159⟩. ⟨hal-00717364⟩

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