Correlation-Induction Techniques for Estimating Quantiles in Simulation Experiments

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Abstract
A simulation-based quantile estimator measures the level of system performance that can be delivered with a prespecified probability. To estimate selected quantiles of the response of a finite-horizon simulation, we develop procedures based on correlation induction techniques for variance reduction, with emphasis on antithetic variates and Latin hypercube sampling. These procedures achieve improved precision by controlling the simulation's random-number inputs as an integral part of the experimental design. The proposed multiple-sample quantile estimator is the average of negatively correlated quantile estimators computed from disjoint samples of the simulation response, where negative correlation is induced between corresponding responses in different samples while mutual independence of responses is maintained within each sample. The proposed single-sample quantile estimator is computed from negatively correlated simulation responses within one all-inclusive sample. The single-sample estimator based on Latin hypercube sampling is shown to be asymptotically normal and unbiased with smaller variance than the comparable direct-simulation estimator based on independent replications. Similar asymptotic comparisons of the multiple-sample and direct-simulation estimators focus on bias and mean square error. Monte Carlo results suggest that the proposed procedures can yield significant reductions in bias, variance, and mean square error when estimating quantiles of the completion time of a stochastic activity network.

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