Accurate calculations of Stationary Distributions and Mean First Passage Times in Markov Renewal Processes and Markov Chains

• Autorzy: Jeffrey J. Hunter
• Języki publikacji: EN

Abstrakty

EN

This article describes an accurate procedure for computing the mean first passage times of a finite irreducible Markov chain and a Markov renewal process. The method is a refinement to the Kohlas, Zeit fur Oper Res, 30, 197–207, (1986) procedure. The technique is numerically stable in that it doesn’t involve subtractions. Algebraic expressions for the special cases of one, two, three and four states are derived.Aconsequence of the procedure is that the stationary distribution of the embedded Markov chain does not need to be derived in advance but can be found accurately from the derived mean first passage times. MatLab is utilized to carry out the computations, using some test problems from the literature.

Słowa kluczowe

EN

Markov chain; Markov renewal process; stationary distribution; mean first passage times

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2016
• Tom: 4
• Numer: 1
• Strony: 151-175

Daty

otrzymano

2015-10-05

zaakceptowano

2016-02-14

online

2016-03-18

Twórcy

autor

Jeffrey J. Hunter

• Department of Mathematical Sciences, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, New Zealand

Bibliografia

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Identyfikatory

DOI

10.1515/spma-2016-0015