Stationary IPA Estimates for Non-Smooth G/G/1/$\infty$ Functionals via Palm Inversion and Level-Crossing Analysis
Probability
2012-07-16 v1
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.
Keywords
Cite
@article{arxiv.1207.3241,
title = {Stationary IPA Estimates for Non-Smooth G/G/1/$\infty$ Functionals via Palm Inversion and Level-Crossing Analysis},
author = {Pierre Bremaud and Jean-Marc Lasgouttes},
journal= {arXiv preprint arXiv:1207.3241},
year = {2012}
}