Importance sampling for the simulation of highly reliable Markovian systems
Management Science
The Combinatorics of Network Reliability
The Combinatorics of Network Reliability
Algorithms in Java, Part 5: Graph Algorithms
Algorithms in Java, Part 5: Graph Algorithms
New measures of robustness in rare event simulation
WSC '05 Proceedings of the 37th conference on Winter simulation
Approximate zero-variance simulation
Proceedings of the 40th Conference on Winter Simulation
Rare Event Simulation using Monte Carlo Methods
Rare Event Simulation using Monte Carlo Methods
Asymptotic robustness of estimators in rare-event simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Dependent failures in highly reliable static networks
Proceedings of the Winter Simulation Conference
Graph reductions to speed up importance sampling-based static reliability estimation
Proceedings of the Winter Simulation Conference
Static Network Reliability Estimation via Generalized Splitting
INFORMS Journal on Computing
International Journal of Metaheuristics
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We study the combination of two efficient rare event Monte Carlo simulation techniques for the estimation of the connectivity probability of a given set of nodes in a graph when links can fail: approximate zero-variance importance sampling and a conditional Monte Carlo method which conditions on the event that a prespecified set of disjoint minpaths linking the set of nodes fails. Those two methods have been applied separately. Here we show how their combination can be defined and implemented, we derive asymptotic robustness properties of the resulting estimator when reliabilities of individual links go arbitrarily close to one, and we illustrate numerically the efficiency gain that can be obtained.