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We give stationary estimates for the derivative of the expectation of anon-smooth function of bounded variation f of the workload in a G/G/1/$\infty$queue, with respect to a parameter influencing the distribu- tion of the inputprocess. For this, we use an idea of Konstantopoulos and Zazanis based on thePalm inversion formula, however avoiding a limiting argument by performing thelevel-crossing analysis thereof globally, via Fubini's theorem. This method ofproof allows to treat the case where the workload distribution has a mass atdiscontinuities of f and where the formula has to be modified. The case wherethe parameter is the speed of service or/and the time scale factor of the inputprocess is also treated using the same approach.

Stationary IPA Estimates for Non-Smooth G/G/1/$\infty$ Functionals via Palm Inversion and Level-Crossing Analysis