An approximation method for complete solutions of Markov-modulated fluid models

Authors:
D. McDonald;K. Qian
Affiliations:
Mathematics Department, University of Ottawa, Ottawa, Ontario, Canada K1N 6N5 E-mail: dmdsg@mathstat.uottawa.ca;BNR, P.O.Box 3511, Station C, Ottawa, Ontario, Canada K1Y 4H7 E-mail: qian@bnr.ca
Venue:
Queueing Systems: Theory and Applications
Year:
1998

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Abstract

This paper presents an approximation method for numerically solving general Markov-modulated fluid models which are widely used in modelling communications and computer systems. We show how the superposition of a group of heterogeneous sources (normally modeled by a multidimensional Markov process) can be approximated by a one-dimensional Markov process, which is then used as the modulating process of the buffer content process. The method effectively reduces the computation that is usually required to find exact (or asymptotic) solutions of fluid models. While this method is general, we focus our discussion on the models with only ON/OFF traffic sources. Numerous numerical results are provided to show the accuracy of the approximation.