The theory of direct probability redistribution and its application to rare event simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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)
Importance sampling for Jackson networks
Queueing Systems: Theory and Applications
Rare Event Simulation using Monte Carlo Methods
Rare Event Simulation using Monte Carlo Methods
The rare event simulation method RESTART: efficiency analysis and guidelines for its application
Network performance engineering
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RESTART is an accelerated simulation technique that allows the evaluation of low probabilities. In this method a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of the rare event is higher. These regions are defined by means of a function of the system state called the importance function. Guidelines for obtaining suitable importance functions and formulas for the importance function of general Jackson networks were provided in previous papers. In this paper, we study networks with Erlang service times and with the rare set defined as the number of customers in a target node exceeding a predefined threshold. The coefficients of the importance functions used here are the same as those obtained with the formula for Jackson networks but multiplied by a constant obtained heuristically. Low probabilities are accurately estimated for different network topologies within short computational time.