Performability Measure for Acyclic Markovian Models Hédi Nabli

Degradable performance of fault-tolerant computer systems has given rise to considerable interest in mathematical models for combined evaluation of performance and reliability. Most of these models are based upon Markov processes. Several methods have been proposed for the computation of the probability distribution of performability upon an interval of time 0; t]. In this paper, two closed form expressions for the performability of \standard" acyclic models and uniform acyclic models are derived. Furthermore, an algorithm with a low polynomial computational complexity is presented and applied to a degradable computer system. Mesure de performabilit e pour des mod eles markoviens acycliques R esum e : Les syst emes multiprocesseurs tol erant les pannes ont donn e un champ d'int er^ et consid erable dans les mod eles math ematiques qui permettent l' evaluation combin ee des aspects de performance et de abilit e. La plupart de ces mod eles sont bas es sur les processus de Markov. Plusieurs m ethodes ont et e d evelopp ees pour le calcul de la distribution de la performabilit e sur un intervalle de temps donn e 0; t]. Dans cet article, nous proposons deux expressions explicites de la mesure de la performabilit e. La premi ere concerne les mod eles acycliques standards, la deuxi eme s'applique a des mod eles sp eciiques que l'on appelle acycliques uniformes. Par ailleurs, un algorithme de faible complexit e temporelle sera pr esent e et appliqu e a un syst eme informatique d egradable.