Steady-state simulation output analysis: MSE-optimal dynamic batch means with parsimonious storage

Yingchieh Yeh, Purdue University

Abstract

We develop theory and methodology to estimate the variance of the sample mean of general steady-state simulation output data, with consideration of statistical efficiency, computational efficiency, and storage requirements. We strive for automatic methods, in that the practitioner needs to provide no algorithmic parameters, including a priori knowledge of the simulation run length. The methodological approach is to batch the output data, without storing individual observations. The batch sizes and the number of batches are increased dynamically as the simulation run length increases. This approach is similar to Dynamic Batch Means (DBM), developed in the author's M.S. thesis, in which batches are combined by collapsing two batches into one with a doubled batch size. In DBM, however, the number of batches does not increase beyond a specified bound. Here, both batch sizes and numbers of batches are dynamically increased with the objective of minimizing the mean squared error (mse) of the variance estimator of the sample mean. We create algorithm DBM-mse, an automatic mse-optimal batching algorithm with parsimonious storage requirements. Our empirical study shows that the storage efficiency obtained costs little in terms of statistical and computational performance. In addition, we study three related topics. First, we correct a conceptual error of Song and Schmeiser concerning the definition of estimator robustness. In particular, we argue that robustness should be based on error in estimating the center of gravity of the data process, not in mse-optimal batch size. Second, we study properties of the center of gravity and construct a new estimator based on the lag-1 autocorrelation of a standardized-time-series area process. Third, we study the relationship between the original data process and the process formed from non-overlapping batch means. The key result is that the product of batch size and center of gravity is a constant, which leads to prebatching variations of existing algorithms.

Degree

Ph.D.

Advisors

Schmeiser, Purdue University.

Subject Area

Operations research|Industrial engineering

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