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

Part of: Stochastic processes Computer system organization

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

[1] Baccelli, F. and Brémaud, P. (1987) Palm Probability and Stationary Queueing Systems. Lecture Notes in Statistics 41, Springer-Verlag, New York.Google Scholar
[2] Brémaud, P. and Vázquez-Abad, F. (1990) On the pathwise computation of derivatives with respect to the rate of a point process: the phantom RPA method. QUEST A 10, 249–270.Google Scholar
[3] Ho, Y. C. and Cao, X. R. (1983) Perturbation analysis and optimization of queueing networks. J. Optim. Theory Appl. 40, 559–582.CrossRefGoogle Scholar
[4] Kamae, T., Krengel, U. and O'Bbien, G. L. (1977) Stochastic inequalities on partially ordered spaces. Ann. Prob. 5, 899–912.CrossRefGoogle Scholar
[5] Reiman, M. I. and Simon, B. (1989) Open queueing systems in light traffic. Math. Operat. Res. 14, 1, 26–59.Google Scholar
[6] Simon, B. (1989) A new estimator of sensitivity measures for simulations based on light traffic theory. ORSA J. Computing 1, 172–180.Google Scholar
[7] Suri, R. (1989) Perturbation analysis: The state of the art and research issues explained via the GI/GI/1 queue. Proc. IEEE 77, 114–137.CrossRefGoogle Scholar