Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
Convergent iterations for computing stationary distributions of markov
SIAM Journal on Algebraic and Discrete Methods
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Numerical methods in Markov chain modeling
Operations Research
Accelerating mean time to failure computations
Performance Evaluation
Performability Modeling with UltraSAN
IEEE Software
SPNP: Stochastic Petri Net Package
PNPM '89 The Proceedings of the Third International Workshop on Petri Nets and Performance Models
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Iterative numerical methods are an important ingredient for the solution of continuous time Markov dependability models of fault-tolerant systems. In this paper we make a numerical comparison of several splitting-based iterative methods. We consider the computation of steady-state reward rate on rewarded models. This measure requires the solution of a singular linear system. We consider two classes of models. The first class includes failure/repair models. The second class is more general and includes the modeling of periodic preventive test of spare components to reduce the probability of latent failures in inactive components. The periodic preventive test is approximated by an Erlang distribution with enough number of stages. We show that for each class of model there is a splitting-based method which is significantly more efficient than the other methods.