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

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.