CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A decomposition approach for stochastic reward net models
Performance Evaluation
PNPM '99 Proceedings of the The 8th International Workshop on Petri Nets and Performance Models
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These days, parallel and distributed state-space generation algorithms allow us to generate Markov chains with hundreds of millions of states. In order to solve such Markov chains for their steady-state behaviour, we typically use iterative algorithms, either on a single machine, or on a cluster of workstations. When dealing with such huge Markov chains, the accuracy of the computed probability vectors becomes a critical issue. In this paper we report on experimental studies of, among others, the impact of different iterative solution techniques, erratic and stagnating convergence, the impact of the state-space ordering, the influence of the processor architecture chosen and the accuracy of the measure of interest, in relation to the accuracy of the individual state probabilities. To say the least, the paper shows that the results from analysing extremely large Markov chains should be "appreciated with care", and, in fact, questions the feasibility of the ambitious "5 nines programs" that some companies have recently started.