The Efficiency of One Long Run Versus Independent Replications in Steady-State Simulation

We evaluate the efficiency of one long run versus independent replications in steady-state discrete-event simulation, assuming that an initial portion of each replication will be deleted to allow the process to approach steady state. We provide supporting evidence in favor of one long run, but we also show that multiple replications can be more efficient. The advantage of one long run increases if the amount deleted increases or if the covariance function decreases more quickly (assuming it is nonnegative and decreasing). Thus, assuming that the amount deleted depends on the way the process approaches steady state, one long run tends to be efficient when the covariance function decays rapidly compared to the rate the process approaches steady state. We also discuss ways to determine the initial portion to delete. We consider the case of an exponential covariance function in detail, and use it as a basis for approximations. We also consider the M/G/\infty queueing model and reflected Brownian motion, the latter as an approximation for the G/G/1 queueing model. For these models starting at the origin, one long run is efficient, but a moderate number of independent replications is essentially equally efficient. In agreement with Kelton and Law (1984), for such examples our analysis only rules out many replications of very short runs.