An experimental study on iterative methods to compute transient solutions of large Markov models

In this article, we report results of an experimental study on six iterative methods to compute the transient probabilities of large Markov models: full matrix exponentiation, forward Euler method, explicit Runge-Kutta methods of order 2 and 4 and Adams-Bashforth multi-steps methods of order 2 and 4. We suggest a simple but efficient implementation of these algorithms. We discuss how to tune their few parameters. We present experimental results that contradict the literature.