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ON THE COMPARISON OF QUEUEING SYSTEMS WITH THEIR FLUID LIMITS

Published online by Cambridge University Press:  10 April 2001

Eitan Altman ,
Tania Jiménez  and
Ger Koole
Eitan Altman
Affiliation:
INRIA, 06902 Sophia Antipolis, France, E-mail: [email protected]
Tania Jiménez
Affiliation:
INRIA, 06902 Sophia Antipolis, France, and, CeSiMo, Universidad de Los Andes, Mérida, Venezuela, E-mail: [email protected]
Ger Koole
Affiliation:
Vrije Universiteit, 1081 HV Amsterdam, The Netherlands, E-mail: [email protected]
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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 15 , Issue 2 , April 2001 , pp. 165 - 178
Copyright
© 2001 Cambridge University Press

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