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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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SPECIALIZED STRUCTURES

SPECIALIZED STRUCTURES

Chapter:
(p.263) 9 SPECIALIZED STRUCTURES
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/9780198527688.003.0009

Some specialized structures are investigated in this chapter and some of the algorithms in previous chapters are adapted to the specific cases. Markov chains with limited displacement (non-skip-free processes) are solved by means of functional iterations and cyclic reduction. Markov chains of M/G/1-type are reduced to a special QBD process with infinite blocks and treated with cyclic reduction. Finally, three different algorithms for tree-like stochastic processes, relying on fixed point iterations, Newton’s iteration, and cyclic reduction, are introduced and analysed.

Keywords:   non-skip-free processes, fixed-point iterations, cyclic reduction, M/G/1-type Markov chains, QBD processes, tree-like processes, Newton’s iteration

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