A successive lumping procedure for a class of markov chains

Michael N. Katehakis, Laurens C. Smit

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

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 2012

All Science Journal Classification (ASJC) codes

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

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