Importance sampling for stochastic simulations
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Importance sampling for the simulation of highly reliable Markovian systems
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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 simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Fast simulation of networks of queues with effective and decoupling bandwidths
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Simulating heavy tailed processes using delayed hazard rate twisting
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Multilevel Splitting for Estimating Rare Event Probabilities
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Importance sampling simulation in the presence of heavy tails
WSC '05 Proceedings of the 37th conference on Winter simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Asymptotic robustness of estimators in rare-event simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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This paper deals with estimating small tail probabilities of the steady-state waiting time in a GI/GI/1 queue with heavy-tailed (subexponential) service times. The problem of estimating infinite horizon ruin probabilities in insurance risk processes with heavy-tailed claims can be transformed into the same framework. It is well-known that naive simulation is ineffective for estimating small probabilities and special fast simulation techniques like importance sampling, multilevel splitting, etc., have to be used. Previous fast simulation techniques for queues with subexponential service times have been confined to M/GI/1 queueing systems. The general approach is to use the Pollaczek-Khintchine transformation to transform the problem into that of estimating the tail distribution of a geometric sum of independent subexponential random variables. However, no such useful transformation exists when one goes from Poisson arrivals to general interarrival-time distributions. We describe an approach that is based on directly simulating the random walk associated with the waiting-time process of the GI/GI/1 queue, using a change of measure called delayed subexponential twisting --- an importance sampling idea recently developed and found useful in the context of M/GI/1 heavy-tailed simulations.