Importance sampling for stochastic simulations
Management Science
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
A Unified Framework for Simulating Markovian Models of Highly Dependable Systems
IEEE Transactions on Computers
Bounded relative error in estimating transient measures of highly dependable non-Markovian systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Importance sampling for the simulation of highly reliable Markovian systems
Management Science
Restart: a straightforward method for fast simulation of rare events
WSC '94 Proceedings of the 26th conference on Winter simulation
Effective bandwidth and fast simulation of ATM intree networks
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
Fast transient simulation of Markovian models of highly dependable systems
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Rare event simulation in stochastic models
WSC '95 Proceedings of the 27th conference on Winter simulation
On the efficiency of the splitting and roulette approach for sensitivity analysis
Proceedings of the 29th conference on Winter simulation
Latin supercube sampling for very high-dimensional simulations
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
A comparison of RESTART implementations
Proceedings of the 30th conference on Winter simulation
Variance reduction in mean time to failure simulations
WSC '88 Proceedings of the 20th conference on Winter simulation
Multilevel Splitting for Estimating Rare Event Probabilities
Operations Research
Variance with alternative scramblings of digital nets
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Fast Simulation of Markov Chains with Small Transition Probabilities
Management Science
Variance Reduction via Lattice Rules
Management Science
On Numerical Problems in Simulations of Highly Reliable Markovian Systems
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
On the efficiency of RESTART for multidimensional state systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
New measures of robustness in rare event simulation
WSC '05 Proceedings of the 37th conference on Winter simulation
Limit theorems for the multilevel splitting algorithm in the simulation of rare events
WSC '05 Proceedings of the 37th conference on Winter simulation
Splitting with weight windows to control the likelihood ratio in importance sampling
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Introduction to Rare Event Simulation
Introduction to Rare Event Simulation
Splitting for rare-event simulation
Proceedings of the 38th conference on Winter simulation
Asymptotic robustness of estimators in rare-event simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Application of the RESTART/Splitting technique to network resilience studies in NS2
MS '08 Proceedings of the 19th IASTED International Conference on Modelling and Simulation
How to generate uniform samples on discrete sets using the splitting method
Probability in the Engineering and Informational Sciences
A variant of importance splitting for rare event estimation: Fixed number of successes
ACM Transactions on Modeling and Computer Simulation (TOMACS)
The rare event simulation method RESTART: efficiency analysis and guidelines for its application
Network performance engineering
Efficient Monte Carlo simulation via the generalized splitting method
Statistics and Computing
Static Network Reliability Estimation via Generalized Splitting
INFORMS Journal on Computing
Splitting for rare event simulation in biochemical systems
Proceedings of the 6th International ICST Conference on Simulation Tools and Techniques
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In the context of rare-event simulation, splitting and importance sampling (IS) are the primary approaches to make important rare events happen more frequently in a simulation and yet recover an unbiased estimator of the target performance measure, with much smaller variance than a straightforward Monte Carlo (MC) estimator. Randomized quasi-Monte Carlo (RQMC) is another class of methods for reducing the noise of simulation estimators, by sampling more evenly than with standard MC. It typically works well for simulations that depend mostly on very few random numbers. In splitting and IS, on the other hand, we often simulate Markov chains whose sample paths are a function of a long sequence of independent random numbers generated during the simulation. In this article, we show that RQMC can be used jointly with splitting and/or IS to construct better estimators than those obtained by either of these methods alone. We do that in a setting where the goal is to estimate the probability of reaching B before reaching (or returning to) A when starting A from a distinguished state not in B, where A and B are two disjoint subsets of the state space, and B is very rarely reached. This problem has several practical applications. The article is in fact a two-in-one: the first part provides a guided tour of splitting techniques, introducing along the way some improvements in the implementation of multilevel splitting. At the end of the article, we also give examples of situations where splitting is not effective. For these examples, we compare different ways of applying IS and combining it with RQMC.