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

In this paper we deal with iterative numerical methods to solve linear syst ems arising in continuous-time Markov chain (CTMC) models. We develop an al gorithm to dynamically tune the relaxation parameter of the successive over -relaxation method. We give a sufficient condition for the Gauss-Seidel met hod to converge when computing the steady-state probability vector of a fin ite irreducible CTMC, and a sufficient condition for the generalized minima l residual projection method not to converge to the trivial solution 0 when computing that vector. Finally, we compare several splitting-based iterati ve methods and a variant of the generalized minimal residual projection met hod. (C)2000 Elsevier Science B.V. All rights reserved.