Multiple comparisons with the best using common random numbers for steady-state simulations

Suppose that there are k≥2 different systems (i.e., stochastic processes), where each system has an unknown steady-state mean performance. We consider the problem of running a single-stage simulation using common random numbers to construct simultaneous confidence intervals for μ_i-max_j≠iμ_j,i=1,2,...,k. This is known as multiple comparisons with the best (MCB). Under an assumption that the stochastic processes representing the simulation output of the different systems satisfy a functional central limit theorem, we prove that our confidence intervals are asymptotically valid (as the run lengths of the simulations of each system tends to infinity). We develop algorithms for two different cases: when the asymptotic covariance matrix has sphericity, and when the covariance matrix is arbitrary.