Numerical iterative methods for Markovian dependability and performability models: new results and a comparison

In this paper we deal with iterative numerical methods to solve linear systems arising in continuous-time Markov chain (CTMC) models. We develop an algorithm to dynamically tune the relaxation parameter of the successive over-relaxation method. We give a sufficient condition for the Gauss–Seidel method to converge when computing the steady-state probability vector of a finite irreducible CTMC, and a sufficient condition for the generalized minimal residual projection method not to converge to the trivial solution 0 when computing that vector. Finally, we compare several splitting-based iterative methods and a variant of the generalized minimal residual projection method.