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

Suppose that we have k different stochastic systems, where /spl mu/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 sys tems, labeled 1,2,...,k - 1, relative to this 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 one sided confidence intervals for/spl mu/i - /spl mu/k (i = 1, 2, . . ., k), each having prespecified (absolute or relative) half width 6. 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 /spl delta/ /spl rarr/ 0 with the size of the batches proportional to 1//spl delta//sup 2/), the joint probability that the confidence intervals simultaneously contain the /spl mu/i - /spl mu/k (i = 1, 2,..., k - 1) is at least 1 - /spl alpha/, where /spl alpha/ is prespecified by the user.