V. Sune et al., Numerical iterative methods for Markovian dependability and performabilitymodels: new results and a comparison, PERF EVAL, 39(1-4), 2000, pp. 99-125
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.