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Closed Form Transient Solution of Continuous Time Markov Chains Through Uniformization

TitleClosed Form Transient Solution of Continuous Time Markov Chains Through Uniformization
Publication TypeConference Paper
Year of Publication2013
AuthorsCerdà-Alabern, L
Conference Name7th International Conference on Performance Evaluation Methodologies and Tools, Valuetools
Date Published12/2013
Conference LocationTorino, Italy
KeywordsEigenvectors method, Markov chains, transient solution, Uniformization., Vandermonde system
Abstract

This paper derives a mapping between a close form transient solution of a continuous time Markov chain (CTMC), and a close form transient solution of one of its uniformized discrete time Markov chains. This result is used to propose a new method to compute the transient solution of CTMCs. The method is simple to implement and has important benefits: (i) It yields a closed-form solution. (ii) It can be used to compute the transient solution for general CTMCs (even with absorbing states, or defective matrices). (iii) It can be used even for chains having a large number of states.

Notes

Best paper award.

URLhttp://valuetools.org/2013/show/home