01096nas a2200169   4500000000100000008004100001260002700042653002400069653001800093653002300111653002000134653002300154100002800177245009100205856004100296520058900337       2013                            d  c12/2013aTorino, Italy10aEigenvectors method10aMarkov chains10atransient solution10aUniformization.10aVandermonde system1 aLlorenç Cerdà-Alabern00aClosed Form Transient Solution of Continuous Time Markov Chains Through Uniformization  uhttp://valuetools.org/2013/show/home3 aThis 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.