Simulation output analysis via dynamic batch means

Abstract

This paper is focused on estimating the quality of the sample mean from a steady-state simulation experiment with consideration of computational efficiency, memory requirement, and statistical efficiency. In addition, we seek methods that do not require knowing run length a priori. We develop an algorithm of nonoverlapping batch means that is implemented in fixed memory by dynamically changing both batch size and number of batches as the simulation runs. The algorithm, denoted by DBM for Dynamic Batch Means, requires computation time similar to other batch means data-collection methods, despite its fixed memory requirement. To achieve satisfactory statistical efficiency of DBM, we propose two associated estimators, V/spl circ//sub TBM/ and V/spl circ//sub PBM/, of the variance of the sample mean and investigate their statistical properties. Our study shows that the estimator V/spl circ//sub PBM/ with parameter w=1 is, as a practical matter, better than the other proposed estimators.