Selecting the best system in steady-state simulations using batch means

Suppose that we want to compare k different systems, where μ _i denotes the steady state mean performance of system i. Our goal is to use simulation to pick the “best” system (i.e., the one with the largest or smallest steady state mean). To do this, we present some two stage procedures based on the method of batch means. Our procedures also construct multiple comparisons with the best (MCB) confidence intervals for μ_i-max_j≠iμ_j , i=1,...,k. Under the assumption of an indifference zone of (absolute or relative) width δ, we can show that asymptotically (as δ→0 with the size of the batches proportional to 1/δ²), the joint probability of correctly selecting the best system and of the MCB confidence intervals simultaneously containing μ_i-max_j≠iμ_j, i=1,...,k, is at least 1-α, where α is prespecified by the user