Variance reduction techniques for simulation with applications to stochastic networks

Athanassios Nikolaos Avramidis, Purdue University

Abstract

Variance reduction techniques are designed to improve the efficiency of stochastic simulations--that is, to reduce the computing effort necessary to obtain some specified precision in simulation-based performance measures. This thesis is concerned with the development and analysis of new variance reduction techniques for finite-horizon simulation experiments and their application to the simulation of stochastic networks. In the first part of the thesis, we concentrate on the variance reduction technique of control variates. We develop a new splitting scheme that yields an unbiased estimator of the mean response and an unbiased estimator of the variance of the first estimator. These statistics are used to construct approximate confidence intervals for the mean response. We also present analytical and empirical performance comparisons of this scheme versus classical control variates. In the second part of the thesis, we develop strategies for integrated use of certain well-known variance reduction techniques to estimate a mean simulation response. Our building blocks are the techniques of conditional expectation, correlation induction, and control variates. Under mild assumptions, we show that each integrated strategy yields an estimator with smaller variance than its constituent techniques yield individually. We also provide asymptotic variance comparisons for integrated strategies involving the correlation induction technique of Latin hypercube sampling. Our Monte Carlo results show that in the simulation of stochastic activity networks, large efficiency gains can be achieved with these integrated variance reduction strategies. In the third part of the thesis, we propose new variance reduction techniques based on correlation induction to estimate quantiles of a simulation response. Both single-sample and multiple-sample estimators are developed. We derive the asymptotic distribution of a single-sample estimator based on Latin hypercube sampling, showing that this estimator is asymptotically more efficient than the direct-simulation estimator. Furthermore, if the response is monotone in the random-number inputs that drive the simulation and satisfies some other mild conditions, then the multiple-sample estimator is shown to have asymptotically smaller mean square error than the direct-simulation estimator. The results of a Monte Carlo study suggest that significant efficiency gains can be achieved when estimating quantiles of the completion time of stochastic activity networks.

Degree

Ph.D.

Advisors

Schmeiser, Purdue University.

Subject Area

Operations research|Industrial engineering|Statistics

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