# 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

### Publication series

Name Isaac Newton Institute for Mathematical Sciences

### 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.
Reijsbergen, D.P. ; de Boer, Pieter-Tjerk ; Scheinhardt, Willem R.W. / Transient Behaviour in Highly Dependable Markovian Systems: New Regimes, Multiple Paths. Eighth International Workshop on Rare-Event Simulation. Cambridge, UK : Isaac Newton Institute for Mathematical Sciences, 2010. pp. 26-27
@inproceedings{1455400802494ba49f0693795795d407,
title = "Transient Behaviour in Highly Dependable Markovian Systems: New Regimes, Multiple Paths",
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.",
keywords = "METIS-270905, IR-72372, asymptotic regimes, EWI-18124, Importance sampling",
author = "D.P. Reijsbergen and {de Boer}, Pieter-Tjerk and Scheinhardt, {Willem R.W.}",
year = "2010",
month = "6",
day = "21",
language = "Undefined",
isbn = "not assigned",
publisher = "Isaac Newton Institute for Mathematical Sciences",
pages = "26--27",
booktitle = "Eighth International Workshop on Rare-Event Simulation",

}

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

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

TY - GEN

T1 - Transient Behaviour in Highly Dependable Markovian Systems: New Regimes, Multiple Paths

AU - Reijsbergen, D.P.

AU - de Boer, Pieter-Tjerk

AU - Scheinhardt, Willem R.W.

PY - 2010/6/21

Y1 - 2010/6/21

N2 - 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.

AB - 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.

KW - METIS-270905

KW - IR-72372

KW - asymptotic regimes

KW - EWI-18124

KW - Importance sampling

M3 - Conference contribution

SN - not assigned

SP - 26

EP - 27

BT - Eighth International Workshop on Rare-Event Simulation

PB - Isaac Newton Institute for Mathematical Sciences

CY - Cambridge, UK

ER -

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