In this thesis, we first present a variance estimation technique based on the standardized time series methodology for steady-state simulations. The proposed variance estimator has competitive bias and variance compared to the existing estimators in the literature. We also present the technique of rebatching to further reduce the bias and variance of our variance estimator. Second, we present two fully sequential indifference-zone procedures to select the best system from a number of competing simulated systems when best is defined by the maximum or minimum expected performance. These two procedures have parabola shaped continuation regions rather than the triangular continuation regions employed in several papers. The rocedures we present accommodate unequal and unknown ariances across systems and the use of common random numbers. However, we assume that basic observations are independent and identically normally distributed. Finally, we present procedures for finding a set of feasible or near-feasible systems among a finite number of simulated systems in the presence of multiple stochastic constraints, especially when the number of systems or constraints is large.

In this thesis, we first show that the performance of ranking and selection (R&S) procedures in steady-state simulations depends highly on the quality of the variance estimates that are used. We study the performance of R&S procedures using three variance estimators --- overlapping area, overlapping Cramer--von Mises, and overlapping modified jackknifed Durbin--Watson estimators --- that show better long-run performance than other estimators previously used in conjunction with R&S procedures for steady-state simulations. We devote additional study to the development of the new overlapping modified jackknifed Durbin--Watson estimator and demonstrate some of its useful properties. Next, we consider the problem of finding the best simulated system under a primary performance measure, while also satisfying stochastic constraints on secondary performance measures, known as constrained ranking and selection. We first present a new framework that allows certain systems to become dormant, halting sampling for those systems as the procedure continues. We also develop general procedures for constrained R&S that guarantee a nominal probability of correct selection, under any number of constraints and correlation across systems. In addition, we address new topics critical to efficiency of the these procedures, namely the allocation of error between feasibility check and selection, the use of common random numbers, and the cost of switching between simulated systems.