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A Logarithmic Reduction Algorithm for Quasi-Birth-Death Processes

Guy Latouche and V. Ramaswami
Journal of Applied Probability
Vol. 30, No. 3 (Sep., 1993), pp. 650-674
DOI: 10.2307/3214773
Stable URL: http://www.jstor.org/stable/3214773
Page Count: 25
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A Logarithmic Reduction Algorithm for Quasi-Birth-Death Processes
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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.

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