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.