Efficient simulation of queues in heavy traffic
ACM Transactions on Modeling and Computer Simulation (TOMACS)
New Estimators For Efficient GI/G/1 Simulation
Probability in the Engineering and Informational Sciences
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Conditional simulation is an efficient variance-reduction method in simulation. Recently, it was applied to a few slowly convergent simulation problems that yielded substantial reduction of the variance. In these applications, the conditional expectations are known or can be computed exactly. We investigate situations where this is not the case; conditional expectations are computed by numerical integration, and are not exact. We construct hybrid simulations that incorporate numerical integration into stochastic conditional simulations. Two key concerns of hybrid simulation are: the effect of the approximation error on the estimator and its computational efficiency. More critically, the pursue of a robust and efficient estimator becomes a real challenge when the integrator has a heavy tail over an infinite interval. We shall resolve both concerns theoretically and provide numerical experiments on queueing simulation and ruin probability estimation to show both the efficiency and quality of our approach.