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

Date
2016-03-18
Authors
Hunter, J
Supervisor
Item type
Journal Article
Degree name
Journal Title
Journal ISSN
Volume Title
Publisher
De Gruyter Open
Abstract

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. A consequence 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.

Description
Keywords
Markov chain; Markov renewal process; Stationary distribution; Mean first passage times
Source
Special Matrices, vol.4(1), pp.151 - 175 (25)
Rights statement
© 2016 J. J. Hunter, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.