Comparisons with a standard in simulation experiments

We consider the problem of comparing a finite number of stochastic systems with respect to a single system (designated as the "standard") via simulati on experiments. The comparison is based on expected performance, and the go al is to determine if any system has larger expected performance than the s tandard, and if so to identify the best of the alternatives. In this paper we provide two-stage experiment design and analysis procedures to solve the problem for a variety of scenarios, including those in which we encounter unequal variances across systems, as well as those in which we use the vari ance reduction technique of common random numbers and it is appropriate to do so. The emphasis is added because in some cases common random numbers ca n be counterproductive when performing comparisons with a standard. We also provide methods for estimating the critical constants required by our proc edures, present a portion of an extensive empirical study, and demonstrate one of the procedures via a numerical example.