Abstract
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.
The title of this paper has been inspired by [11].
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Bell, A., Haverkort, B.R. (2007). Untold Horrors About Steady-State Probabilities: What Reward-Based Measures Won’t Tell About the Equilibrium Distribution. In: Wolter, K. (eds) Formal Methods and Stochastic Models for Performance Evaluation. EPEW 2007. Lecture Notes in Computer Science, vol 4748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75211-0_2
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DOI: https://doi.org/10.1007/978-3-540-75211-0_2
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