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A SUCCESSIVE LUMPING PROCEDURE FOR A CLASS OF MARKOV CHAINS

Published online by Cambridge University Press:  30 July 2012

Michael N. Katehakis  and
Laurens C. Smit
Michael N. Katehakis
Affiliation:
Department of Management Science and Information Systems, Rutgers Business School, Newark and New Brunswick, Newark, NJ 07210 E-mail: [email protected]
Laurens C. Smit
Affiliation:
Mathematisch Instituut, Universiteit Leiden, Niels Bohrweg 1, 2333 CA, The Netherlands E-mail: [email protected]
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Abstract

A class of Markov chains we call successively lumbaple is specified for which it is shown that the stationary probabilities can be obtained by successively computing the stationary probabilities of a propitiously constructed sequence of Markov chains. Each of the latter chains has a(typically much) smaller state space and this yields significant computational improvements. We discuss how the results for discrete time Markov chains extend to semi-Markov processes and continuous time Markov processes. Finally, we will study applications of successively lumbaple Markov chains to classical reliability and queueing models.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 4 , October 2012 , pp. 483 - 508
Copyright
Copyright © Cambridge University Press 2012

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