Light-traffic approximations for Markov-modulated multi-server queues

Abstract

A general concept is considered of expanding the expectation of a wide class of functional of marked point processes, which expresses this expectation by a sum of integrals over higher-order factorial moment measures of the underlying point process. The idea of factorial moment expansion is applied in order to derive approximation formulas for stationary characteristics of multi-server queues with Markov-modulated arrival process and with the first-come-first-served queueing discipline. Besides real-valued queueing characteristics like waiting time and total work load, we also give approximations for the Kiefer-Wolfowitz work-load vector. A boundedness condition on the service time distributions is given which ensures that the components of the expected stationary work-load vector are analytic functions of the arrival intensity in a neighborhood of zero. If the service times have phase-type distributions, the factorial moment expansion provides a useful computational technique for approximations of moments of the stationary work-load vector. Some numerical examples are given which show how the algorithm works in light traffic

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