Abstract
Markov chains and rewards have been widely used to evaluate performance, dependability and performability characteristics of computer systems and networks. Despite considerable works, the numerical analysis of Markov chains to obtain transient or steady-state distribution is still a difficult problem when the chain is large or the eigenvalues badly distributed. Thus bounding techniques have been proposed for long to analyze steady-state distribution.
Here, we show how to bound some dependability characteristics such as steady-state and point availability using an algorithmic approach. The bound is based on stochastic comparison of Markov chains but it does not use sample-path arguments. The algorithm builds a lumped Markov chain whose steady-state or transient distributions are upper bounds in the strong stochastic sense of the exact distributions. In this paper, the implementation of algorithm is detailed and we show some numerical results. We also show how we can avoid the generation of the state space and the transition matrix to model chains with more than 1010 states.
This work is supported by ACI Sécurité, project Sure-Paths.
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Bušić, A., Fourneau, J.M. (2005). Bounds for Point and Steady-State Availability: An Algorithmic Approach Based on Lumpability and Stochastic Ordering. In: Bravetti, M., Kloul, L., Zavattaro, G. (eds) Formal Techniques for Computer Systems and Business Processes. EPEW WS-FM 2005 2005. Lecture Notes in Computer Science, vol 3670. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549970_8
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DOI: https://doi.org/10.1007/11549970_8
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