ANZIAM  J.  46 (2005), 485-493

Ramaswami's duality and probabilistic algorithms for determining the rate matrix for a structured GI / M / 1 Markov chain

Emma Hunt   School of Mathematical Sciences   The University of Adelaide   Adelaide SA 5005   Australia     emma.hunt@adelaide.edu.au

Abstract

We show that Algorithm H* for the determination of the rate matrix of a block-GI / M / 1 Markov chain is related by duality to Algorithm H for the determination of the fundamental matrix of a block-M / G / 1 Markov chain. Duality is used to generate some efficient algorithms for finding the rate matrix in a quasi-birth-and-death process.

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