A Unified Framework for Simulating Markovian Models of Highly Dependable Systems
IEEE Transactions on Computers
Restart: a straightforward method for fast simulation of rare events
WSC '94 Proceedings of the 26th conference on Winter simulation
A framework for rare event simulation of stochastic Petri nets using “RESTART”
WSC '96 Proceedings of the 28th conference on Winter simulation
The RESTART/LRE method for rare event simulation
WSC '96 Proceedings of the 28th conference on Winter simulation
A comparison of RESTART implementations
Proceedings of the 30th conference on Winter simulation
The theory of direct probability redistribution and its application to rare event simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient simulation of a tandem Jackson network
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Implementation of Importance Splitting Techniques in Stochastic Petri Net Package
TOOLS '00 Proceedings of the 11th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
Multilevel Splitting for Estimating Rare Event Probabilities
Operations Research
On the efficiency of RESTART for multidimensional state systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Rare events, splitting, and quasi-Monte Carlo
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Stochastic Discrete Event Systems: Modeling, Evaluation, Applications
Stochastic Discrete Event Systems: Modeling, Evaluation, Applications
Rare Event Simulation using Monte Carlo Methods
Rare Event Simulation using Monte Carlo Methods
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
RESTART simulation of networks of queues with Erlang service times
Winter Simulation Conference
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This paper is a tutorial on RESTART, a widely applicable accelerated simulation technique for estimating rare event probabilities. The method is based on performing a number of simulation retrials when the process enters regions of the state space where the chance of occurrence of the rare event is higher. The paper analyzes its efficiency, showing formulas for the variance of the estimator and for the gain obtained with respect to crude simulation, as well as for the parameter values that maximize this gain. It also provides guidelines for achieving a high efficiency when it is applied. Emphasis is placed on the choice of the importance function, i.e., the function of the system state used for determining when retrials are made. Several examples on queuing networks and ultra reliable systems are exposed to illustrate the application of the guidelines and the efficiency achieved.