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Closed Form Transient Solution of Continuous Time Markov Chains Through Uniformization


The code is available in github . You can get it executing

git clone


Implementation of the algorithm described in the paper:

Llorenç Cerdà-Alabern. Closed form transient solution of continuous time markov chains through uniformization. In 7th International Conference on Performance Evaluation Methodologies and Tools, Valuetools, Torino, Italy, December 10–12, 2013. Best paper award.

The method is also described in the public technical report:

Llorenç Cerdà-Alabern. Transient Solution of Markov Chains Using the Uniformized Vandermonde Method. Technical Report UPC-DAC-RR-XCSD-2010-2, Universitat Politècnica de Catalunya, December, 2010. pdf.


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.


Llorenç Cerdà-Alabern.