On the estimation of optimal batch sizes in the analysis of simulation output

The estimation of the variance of point estimators is a classical problem of stochastic simulation. A more specific problem addresses the estimation of the variance of a sample mean from a steady-state autocorrelated process. Many proposed estimators of the variance of the sample mean are parameterized by batch size. A critical problem is to find an appropriate batch size that provides a good tradeoff between bias and variance. This paper proposes a procedure for determining the optimal batch size to minimize the mean squared error of estimators of the variance of the sample mean. This paper also presents the results of empirical studies of the procedure. The experiments involve symmetric two-state Markov chain models, first-order autoregressive processes, seasonal autoregressive processes, and queue-waiting times for several M/M/1 queueing models. The empirical results indicate that the estimation procedure works nearly as well as it would if the parameters of the processes were known.