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This paper is concerned with computing large-deviation asymptotics for the loss process in a stylized queueing model that is fed by a Brownian input process. In addition, the dynamics of the queue, conditional on such a large deviation in the loss, is calculated. Finally, the paper computes the quasi-stationary distribution of the system and the corresponding dynamics, conditional on no loss occurring.

Classical ranking-and-selection (R&S) procedures cannot be applied directly to select the best decision in the presence of distributional ambiguity. In this paper we propose a robust selection-of-the-best (RSB) formulation which compares decisions based on their worst-case performances over a finite set of possible distributions and selects the decision with the best worst-case performance. To solve the RSB problems, we design two-layer R&S procedures, either two-stage or fully sequential, under the indifference-zone formulation. The procedure identifies the worst-case distribution in the first stage and the best decision in the second. We prove the statistical validity of these procedures and test their performances numerically. 868978-1-4799-3950-3/13/$31.00 ©2013 IEEE

Specifying a proper input distribution is often a challenging task in simulation modeling. In practice, there may be multiple plausible distributions that can fit the input data reasonably well, especially when the data volume is not large. In this paper, we consider the problem of selecting the best from a finite set of simulated alternatives, in the presence of such input uncertainty. We model such uncertainty by an ambiguity set consisting of a finite number of plausible input distributions, and aim to select the alternative with the best worst-case mean performance over the ambiguity set. We refer to this problem as robust selection of the best (RSB). To solve the RSB problem, we develop a two-stage selection procedure and a sequential selection procedure; we then prove that both procedures can achieve at least a user-specified probability of correct selection under mild conditions. Extensive numerical experiments are conducted to investigate the computational efficiency of the two procedures. Finally, we apply the RSB approach to study a queueing system's staffing problem using synthetic data and an appointment-scheduling problem using real data from a large hospital in China. We find that the RSB approach can generate decisions significantly better than other widely used approaches.