Analysis of initial transient deletion for parallel steady-state simulations

This paper investigates theoretical properties of a simple method for using parallel processors in discrete event simulations: running independent replications, in parallel, on multiple processors and averaging the results at the end of the runs. Specifically, the problem of estimating steady-state parameters from such an experiment is considered. Sampling plans are considered in which the replication lengths are given by limits on either simulated or computer time, and in which the beginning portion of each run may be deleted for the purpose of controlling initialization bias. The critical relative growth rates for the number of processors, the length of each replication, and the length of the deletion period that are required in order to produce valid confidence intervals for steady-state parameters are determined. When the replication length is determined by computer time, the straightforward estimator with deletion may not work for a large number of processors. In this case, the deletion is essentially useless due to an additional bias term that arises because the simulated time at the end of a replication is random. In this case, a new estimator can be used to remove this source of bias.