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

  • F. Baccelli (a1) and P. Brémaud (a2)

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.

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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.

References

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[1] Baccelli, F. and Brémaud, P. (1987) Palm Probability and Stationary Queueing Systems. Lecture Notes in Statistics 41, Springer-Verlag, New York.
[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, 249270.
[3] Ho, Y. C. and Cao, X. R. (1983) Perturbation analysis and optimization of queueing networks. J. Optim. Theory Appl. 40, 559582.
[4] Kamae, T., Krengel, U. and O'Bbien, G. L. (1977) Stochastic inequalities on partially ordered spaces. Ann. Prob. 5, 899912.
[5] Reiman, M. I. and Simon, B. (1989) Open queueing systems in light traffic. Math. Operat. Res. 14, 1, 2659.
[6] Simon, B. (1989) A new estimator of sensitivity measures for simulations based on light traffic theory. ORSA J. Computing 1, 172180.
[7] Suri, R. (1989) Perturbation analysis: The state of the art and research issues explained via the GI/GI/1 queue. Proc. IEEE 77, 114137.

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

  • F. Baccelli (a1) and P. Brémaud (a2)

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