Transient Behaviour in Highly Dependable Markovian Systems: New Regimes, Multiple Paths

In recent years, probabilistic analysis of highly dependable Markovian systems has received considerable attention. Such systems typically consist of several component types, subject to failures, with spare components for replacement while repair is taking place. System failure occurs when all (spare) components of one or several types have failed. In this work we try to estimate the probability of system failure before some fixed time bound $\tau$ via stochastic simulation. Obviously, in a highly dependable system, system failure is a rare event, so we apply importance sampling (IS) techniques, based on knowledge of the behaviour of the system and the way the rare event occurs. In our talk we discern several interesting ways in which the rare event can occur, each of which has its own way of affecting the efficiency of an importance sampling technique.