ON THE COMPARISON OF QUEUEING SYSTEMS WITH THEIR FLUID LIMITS

Authors:
Eitan Altman;Tania Jiménez;Ger Koole
Affiliations:
INRIA, 06902 Sophia Antipolis, France, E-mail: altman@sophia.inria.fr;INRIA, 06902 Sophia Antipolis, France, and, CeSiMo, Universidad de Los Andes, Mérida, Venezuela, E-mail: tania@ula.ve;Vrije Universiteit, 1081 HV Amsterdam, The Netherlands, E-mail: koole@cs.vu.nl
Venue:
Probability in the Engineering and Informational Sciences
Year:
2001

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Abstract

In this article, we study a method to compare queueing systems and their fluid limits. For a certain class of queueing systems, it is shown that the expected workload (and certain functions of the workload) is higher in the queueing system than in the fluid approximation. This class is characterized by convexity of the value function in the state component(s) where external arrivals occur. The main example that we consider is a tandem of multiserver queues with general service times and Markov-modulated arrivals. The analysis is based on dynamic programming and the use of phase-type distributions. Numerical examples to illustrate the results are also given.