Two-stage procedures for multiple comparisons with a control in steady-state simulations

Suppose that we have k different stochastic systems, where μ_i denotes the steady-state mean of system i. We assume that the system labeled k is a control and want to compare the performance of the other systems, labeled 1,2,...,k-1, relative to the control. This problem is known in the statistical literature as multiple comparisons with a control (MCC). Independent steady-state simulations will be performed to compare the systems to the control. Two-stage procedures, based on the method of batch means, are presented to construct simultaneous lower onesided confidence intervals for μ_i - μ_k (i = 1, 2, ..., k), each having prespecified (absolute or relative) halfwidth δ. Under the assumption that the stochastic processes representing the evolution of the systems satisfy a functional central limit theorem, it can be shown that asymptotically (as δ → 0 with the size of the batches proportional to 1/δ²), the joint probability that the confidence intervals simultaneously contain the μ_i - μ_k (i =/ 1, 2, ..., k-1) is at least 1 - α, where α is prespecified by the user.