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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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M/G/1-TYPE MARKOV CHAINS

M/G/1-TYPE MARKOV CHAINS

Chapter:
(p.89) 4 M/G/1-TYPE MARKOV CHAINS
Source:
Numerical Methods for Structured Markov Chains
Author(s):

D. A. Bini

G. Latouche

B. Meini

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198527688.003.0004

This chapter is devoted to the theoretical analysis of M/G/1-type Markov chains. Conditions for the ergodicity are given in terms of the drift. The reduction to solving a nonlinear matrix equation is shown and the role played by canonical factorizations in this regard is pointed out. The Ramaswami formula for the computation of the stationary distribution is revisited in terms of canonical factorizations.

Keywords:   nonsslinear matrix equations, ergodicity, canonical factorization, Ramaswami formula, stationary distribution

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