On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
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
Simulating heavy tailed processes using delayed hazard rate twisting
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Appendix: A primer on heavy-tailed distributions
Queueing Systems: Theory and Applications
A unified approach for finite-dimensional, rare-event Monte Carlo simulation
WSC '04 Proceedings of the 36th conference on Winter simulation
Optimizing portfolio tail measures: asymptotics and efficient simulation optimization
Proceedings of the 40th Conference on Winter Simulation
Confidence intervals for quantiles when applying variance-reduction techniques
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Using sectioning to construct confidence intervals for quantiles when applying importance sampling
Proceedings of the Winter Simulation Conference
Asymptotic properties of kernel density estimators when applying importance sampling
Proceedings of the Winter Simulation Conference
Confidence intervals for quantiles and value-at-risk when applying importance sampling
Proceedings of the Winter Simulation Conference
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We derive tail asymptotics for the probability that the maximum of sums of a few random variables exceeds an increasing threshold, when the random variables may be light as well as heavy tailed. These probabilities arise in many applications including in PERT networks where our interest may be in measuring the probability of large project delays. We also develop provably asymptotically optimal importance sampling techniques to efficiently estimate these probabilities. In the light-tailed settings we show that an appropriate mixture of exponentially twisted distributions efficiently estimates these probabilities. As is well known, exponential twisting based methods are not applicable in the heavy-tailed settings. To remedy this, we develop techniques that rely on “asymptotic hazard rate twisting” and prove their effectiveness in both light and heavy-tailed settings. We show that in many cases the latter may have implementation advantages over exponential twisting based methods in the light-tailed settings. However, our experiments suggest that when easily implementable, the exponential twisting based methods significantly outperform asymptotic hazard rate twisting based methods.