Closed Form Transient Solution of Continuous Time Markov Chains Through Uniformization

Llorenç Cerdà-Alabern

7th International Conference on Performance Evaluation Methodologies and Tools

Research Article

Closed Form Transient Solution of Continuous Time Markov Chains Through Uniformization

Cite: BibTeX Plain Text

@INPROCEEDINGS{10.4108/icst.valuetools.2013.254376,
    author={Lloren\`{e} Cerd\'{a}-Alabern},
    title={Closed Form Transient Solution of Continuous Time Markov Chains Through Uniformization},
    proceedings={7th International Conference on Performance Evaluation Methodologies and Tools},
    publisher={ICST},
    proceedings_a={VALUETOOLS},
    year={2014},
    month={1},
    keywords={markov chains transient solution eigenvectors method vandermonde system uniformization},
    doi={10.4108/icst.valuetools.2013.254376}
}

Llorenç Cerdà-Alabern
Year: 2014
Closed Form Transient Solution of Continuous Time Markov Chains Through Uniformization
VALUETOOLS
ACM
DOI: 10.4108/icst.valuetools.2013.254376

Llorenç Cerdà-Alabern¹^,*

1: Universitat Politècnica de Catalunya

*Contact email: llorenc@ac.upc.edu

Abstract

This paper derives a mapping between a closed form transient solution of a continuous time Markov chain (CTMC), and a closed 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.

Keywords: markov chains transient solution eigenvectors method vandermonde system uniformization

Published: 2014-01-09
Publisher: ICST

: http://dx.doi.org/10.4108/icst.valuetools.2013.254376