The Allocation of Computer Time in Comparing Simulation Experiments

This paper investigates the problem of efficiently allocating computer time between two simulation experiments when the objective is to make a statistical comparison of means. For a given level of accuracy our results show that significantly less computer time is required when the sample sizes are determined according to a certain rule than when the sample sizes are equal. A graphical analysis suggests that small errors in estimating the population parameters of the allocation rule do not significantly affect the efficient allocation of time. The influence that the degree of autocorrelation has on the time allocation is also investigated; results show that small differences in the autocorrelation functions are important when each process is highly autocorrelated. Positively correlated samples for the two experiments are examined and incorporated into the efficient allocation rule. It is shown that their use leads to a saving in computer time. A two-stage procedure is described wherein initial estimates of the population parameters are computed which permit the experimenter to estimate how many more observations to collect on each experiment. The procedure is simple and straightforward to implement and should be of practical value. When the computer time requirements turn out to be prohibitive, we suggest using negatively correlated replications on each experiment. This may be accomplished by using antithetic variates. The two-stage procedure also applies in this case.