In this thesis, there are generally three contributions to the Ranking and Selection problem in discrete-event simulation area. Ranking and selection is an important problem when people want to select single or multiple best designs from alternative pool.
There are two different types in discrete-event simulation: terminating simulation and steady-state simulation. For steady-state simulation, there is an initial trend before the data output enters into the steady-state, if we cannot start the simulation from steady state. We need to remove the initial trend before we use the data to estimate the steady-state mean. Our first contribution regards the application to eliminate the initial trend/initialization bias. In this thesis, we present a novel solution to remove the initial trend motivated by offline change detection method. The method is designed to monitor the cumulative absolute bias from the estimated steady-state mean. Experiments are conducted to compare our procedure with other existing methods. Our method is shown to be at least no worse than those methods and in some cases much better. After removing the initialization bias, we can apply a ranking and selection procedure for the data outputs from steady-state simulation.
There are two main approaches to ranking and selection problem. One is subset selection and the other one is indifference zone selection. Also by employing directed graph, some single-best ranking and selection methods can be extended to solve multi-best selection problem. Our method is designed to solve multi-best ranking and selection. And in Chapter 3, one procedure for ranking and selection in terminating simulation is extended based full sequential idea. It means we compare the sample means among all systems in contention at each stage. Also, we add a technique to do pre-selection of the superior systems at the same time of eliminating inferior systems. This can accelerate the speed of obtaining the number of best systems we want. Experiments are conducted to demonstrate the pre-selection technique can save observation significantly compared with the procedure without it. Also compared with existing methods, our procedure can save significant number of observations. We also explore the effect of common random number. By using it in the simulation process, more observations can be saved.
The third contribution of this thesis is to extend the procedure in Chapter 3 for steady-state simulation. Asymptotic variance is employed in this case. We justify our procedure in asymptotic point of view. And by doing extensive experiments, we demonstrate that our procedure can work in most cases when sample size is finite