Selecting small quantiles

Ranking and selection (R&S) techniques are statistical methods developed to select the best system, or a subset of systems from among a set of alternative system designs. R&S via simulation is particularly appealing as it combines modeling flexibility of simulation with the efficiency of statistical techniques for effective decision making. The overwhelming majority of the R&S research, however, focuses on the expected performance of competing designs. Alternatively, quantiles, which provide additional information about the distribution of the performance measure of interest, may serve as better risk measures than the usual expected value. In stochastic systems, quantiles indicate the level of system performance that can be delivered with a specified probability. In this paper, we address the problem of ranking and selection based on quantiles. In particular, we formulate the problem and characterize the optimal budget allocation scheme using the large deviations theory.