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.