Approximate solutions for heavily loaded Markov-modulated queues

Authors:
Isi Mitrani
Affiliations:
School of Computing Science, University of Newcastle, Newcastle upon Tyne, NE1 7RU, United Kingdom
Venue:
Performance Evaluation - Performance 2005
Year:
2005

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Abstract

The existing exact solutions for Markov-modulated queues are computationally intensive and prone to numerical problems when the number of states of the Markovian environment becomes large. To address this problem, a simple geometric approximation is proposed. It uses the dominant eigenvalue of the characteristic matrix polynomial, together with the associated left eigenvector. That approximation is shown to be asymptotically exact in heavy traffic. In other cases, its accuracy is examined numerically.