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

摘要

This article describes an accurate procedure for computing the mean first passage times of a finiteirreducible Markov chain and a Markov renewal process. The method is a refinement to the Kohlas, Zeit furOper 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.Aconsequenceof the procedure is that the stationary distribution of the embedded Markov chain does not need to be derivedin advance but can be found accurately from the derived mean first passage times. MatLab is utilized to carryout the computations, using some test problems from the literature.