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

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademic

### Abstract

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.
Original language Undefined Eighth International Workshop on Rare-Event Simulation Cambridge, UK Isaac Newton Institute for Mathematical Sciences 26-27 2 not assigned Published - 21 Jun 2010 8th International Workshop on Rare-Event Simulation, RESIM 2010 - Cambridge, UK, Cambridge, United KingdomDuration: 21 Jun 2010 → 23 Jun 2010Conference number: 8

### Publication series

Name Isaac Newton Institute for Mathematical Sciences

### Workshop

Workshop 8th International Workshop on Rare-Event Simulation, RESIM 2010 RESIM United Kingdom Cambridge 21/06/10 → 23/06/10 21-23 June 2010

### Keywords

• METIS-270905
• IR-72372
• asymptotic regimes
• EWI-18124
• Importance sampling

### Cite this

Reijsbergen, D. P., de Boer, P-T., & Scheinhardt, W. R. W. (2010). Transient Behaviour in Highly Dependable Markovian Systems: New Regimes, Multiple Paths. In Eighth International Workshop on Rare-Event Simulation (pp. 26-27). Cambridge, UK: Isaac Newton Institute for Mathematical Sciences.