  In this paper, we study three asymptotic regimes that can be applied to
ranking and selection (R&S) problems with general sample distributions. These
asymptotic regimes are constructed by sending particular problem parameters
(probability of incorrect selection, smallest difference in system performance
that we deem worth detecting) to zero. We establish asymptotic validity and
efficiency of the corresponding R&S procedures in each regime. We also analyze
the connection among different regimes and compare the pre-limit performances
of corresponding algorithms.
