A Multi-Level Method for the Steady State Solution of Markov Chains

This paper illustrates the current state of development of an algorithm for the steady state solution of continuous-time Markov chains. The so-called multi-level algorithm utilizes ideas from algebraic multigrid to provide an efficient alternative to the currently used Gauss-Seidel and successive overrelaxation methods. The multi-level method has been improved through several iterations, so that it is now able to solve several classes of Markov chains robustly and efficiently. Among these are Markov chains with heterogeneous transition rates and ones with almost identical transition rates. Experiments were used to verify the improvements throughout the iterations and the advantages in comparison to the usual methods.