A successive lumping procedure for a class of markov chains

Michael N. Katehakis, Laurens C. Smit

Research output: Contribution to journalArticle

15 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)483-508
Number of pages26
JournalProbability in the Engineering and Informational Sciences
Volume26
Issue number4
DOIs
StatePublished - Oct 1 2012

Fingerprint

Markov processes
Markov chain
Continuous-time Markov Process
Semi-Markov Process
Queueing Model
State Space
Discrete-time
Class
Computing

All Science Journal Classification (ASJC) codes

  • Industrial and Manufacturing Engineering
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research

Cite this

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A successive lumping procedure for a class of markov chains. / Katehakis, Michael N.; Smit, Laurens C.

In: Probability in the Engineering and Informational Sciences, Vol. 26, No. 4, 01.10.2012, p. 483-508.

Research output: Contribution to journalArticle

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