Bounds for point and steady state availability

Niveau: Secondaire, Lycée, Terminale
Bounds for point and steady-state availability: an algorithmi approa h based on lumpability and sto hasti ordering A. Busi and J.M. Fourneau PRiSM, Universite de Versailles-Saint-Quentin, 45, Av. des Etats-Unis 78000 Versailles, Fran e Abstra t. Markov hains and rewards have been widely used to eval- uate performan e, dependability and performability hara teristi s of omputer systems and networks. Despite onsiderable works, the nu- meri al analysis of Markov hains to obtain transient or steady-state distribution is still a diÆ ult problem when the hain is large or the eigenvalues badly distributed. Thus bounding te hniques have been pro- posed for long to analyze steady-state distribution. Here, we show how to bound some dependability hara teristi s su h as steady-state and point availability using an algorithmi approa h. The bound is based on sto hasti omparison of Markov hains but it does not use sample-path arguments. The algorithm builds a lumped Markov hain whose steady-state or transient distributions are upper bounds in the strong sto hasti sense of the exa t distributions. In this paper, the implementation of algorithm is detailed and we show some numeri al results. We also show how we an avoid the generation of the state spa e and the transition matrix to model hains with more than 10 10 states.

• has been


• matrix whi


• between up


• sto hasti


• state distribution


• markov hains


• transition matrix


• theoreti al