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Numerical Methods for Structured Markov Chains$
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Dario A. Bini, Guy Latouche, and Beatrice Meini

Print publication date: 2005

Print ISBN-13: 9780198527688

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198527688.001.0001

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Numerical Methods for Structured Markov Chains

D. A. Bini

G. Latouche

B. Meini

Oxford University Press

In this chapter a series of processes with a variety of transition structures are considered and their analysis is presented in a unifying manner. These processes are grouped under the generic name of Phase-type queues, they include G/M/1-type Markov chains, QBD processes, Markov chains with Toeplitz-like transitions and limited displacements (non-skip-free), and tree-like processes. A duality property between M/G/1 and G/M/1 Markov chains is described and a reduction of M/G/1 and G/M/1 Markov chains to QBD is analysed.

Keywords:   G/M/1-type Markov chains, QBD processes, tree-like processes, limited displacement, non-skip-free processes, duality property

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