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A logarithmic reduction algorithm for quasi-birth-death processes

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Guy Latouche  and
V. Ramaswami
Guy Latouche*
Affiliation:
Université Libre de Bruxelles
V. Ramaswami*
Affiliation:
Bellcore
*
∗ Postal address: Université Libre de Bruxelles, Département d'Informatique, CP212, Boulevard du Triomphe, 1050 Bruxelles, Belgium.
∗∗ Postal address: Bellcore, 331 Newman Springs Road, Red Bank, NJ 07701–7030, USA.
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Abstract

Quasi-birth-death processes are commonly used Markov chain models in queueing theory, computer performance, teletraffic modeling and other areas. We provide a new, simple algorithm for the matrix-geometric rate matrix. We demonstrate that it has quadratic convergence. We show theoretically and through numerical examples that it converges very fast and provides extremely accurate results even for almost unstable models.

Keywords

QUEUEING THEORYMATRIX METHODSCOMPUTATIONAL PROBABILITYQUADRATIC CONVERGENCEFIRST-PASSAGE TIMES

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J05: Discrete-time Markov processes on general state spaces 60K25: Queueing theory

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 3 , September 1993 , pp. 650 - 674
Copyright
Copyright © Applied Probability Trust 1993 

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