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Virtual customers in sensitivity and light traffic analysis via Campbell's formula for point processes

Part of: Computer system organization Stochastic processes

Published online by Cambridge University Press:  01 July 2016

F. Baccelli  and
P. Brémaud
F. Baccelli*
Affiliation:
INRIA Sophia-Antipolis
P. Brémaud*
Affiliation:
Laboratoire des Signaux et Systèmes, CNRS
*
∗Postal address: INRIA Sophia-Antipolis, 2004 Route des Lucioles, BP 109, 06561 Valbonne Cedex, France.
∗∗Postal address: Laboratoire des Signaux et Systèmes, CNRS-ESE, Plateau du Moulon, 91190 Gif sur Yvette Cedex, France.
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Abstract

This article provides the theoretical basis of the virtual customer method or positive rare perturbation (RPA) method of sensitivity analysis, and in particular gives a short proof of the light traffic derivative result of Reiman and Simon [5] based on Campbell's formula. As a by-product, we obtain the archetypal H = λG formula associated with a stationary quantity of a queueing system.

Keywords

POSITIVE RARE PERTURBATIONH = λG

MSC classification

Primary: 60G55: Point processes
Secondary: 68M20: Performance evaluation; queueing; scheduling
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 1 , March 1993 , pp. 221 - 234
Copyright
Copyright © Applied Probability Trust 1993 

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References

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