Steady-State Analyses: Variance Estimation in Simulations and Dynamic Pricing in Service Systems
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In this dissertation, we consider analytic and numeric approaches to the solution of probabilistic steady-state problems with specific applications in simulation and queueing theory. Our first objective on steady-state simulations is to develop new estimators for the variance parameter of a selected output process that have better performance than certain existing variance estimators in the literature. To complete our analysis of these new variance estimators, called linear combinations of overlapping variance estimators, we do the following: establish theoretical asymptotic properties of the new estimators; test the theoretical results on a battery of examples to see how the new estimators perform in practice; and use the estimators for confidence interval estimation for both the mean and the variance parameter. Our theoretical and empirical results indicate the new estimators' potential for improvements in accuracy and computational efficiency. Our second objective on steady-state simulations is to derive the expected values of various competing estimators for the variance parameter. In this research, we do the following: formulate the machinery to calculate the exact expected value of a given estimator for the variance parameter; calculate the exact expected values of various variance estimators in the literature; compute these expected values for certain stochastic processes with complicated covariance functions; and derive expressions for the mean squared error of the estimators studied herein. We find that certain standardized time series estimators outperform their competitors as the sample size becomes large. Our research on queueing theory focuses on pricing of the service provided to individual customers in a queueing system. We find sensitivity results that enable efficient computational procedures for dynamic pricing decisions for maximizing the long-run average reward in a queueing facility with the following properties: there are a fixed number of servers, each with the same constant service rate; the system has a fixed finite capacity; the price charged to a customer entering the system depends on the number of customers in the system; and the customer arrival rate depends on the current price of the service. We show that the sensitivity results considered significantly reduce the computational requirements for finding the optimal pricing policies.