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.
Publié le : 1993-07-05
Classification:
level-crossing analysis,
sensitivity analysis,
perturbation analysis,
point processes,
Palm distributions,
level-crossing analysis.,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00717364,
author = {Bremaud, Pierre and Lasgouttes, Jean-Marc},
title = {Stationary IPA Estimates for Non-Smooth G/G/1/$\infty$ Functionals via Palm Inversion and Level-Crossing Analysis.},
journal = {HAL},
volume = {1993},
number = {0},
year = {1993},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00717364}
}
Bremaud, Pierre; Lasgouttes, Jean-Marc. Stationary IPA Estimates for Non-Smooth G/G/1/∞ Functionals via Palm Inversion and Level-Crossing Analysis.. HAL, Tome 1993 (1993) no. 0, . http://gdmltest.u-ga.fr/item/hal-00717364/