Thirty years of “Batch Size Effects”

The method of non-overlapping batch means is the standard for constructing a confidence interval for the mean of a steady-state simulation output. In “Batch Size Effects in the Analysis of Simulation Output,” published in Operations Research in 1982, Schmeiser recast the problem of selecting a batch size by examining the marginal benefit of attaining the largest number of batches (smallest batch size) that still yields a valid confidence interval. His formulation of the problem, and the conclusions he reached, influenced nearly all later work on batching and batching algorithms for confidence-interval estimation.