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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access March 18, 2016

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

  • Jeffrey J. Hunter
From the journal Special Matrices


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.


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Received: 2015-10-5
Accepted: 2016-2-14
Published Online: 2016-3-18

©2016 Jeffrey J. Hunter

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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