Some Tactical Problems in Digital Simulation

Abstract

This paper is concerned with the manner in which an investigation by simulated experimentation is conducted, after the model has been formulated and the computer program completed. It considers the problem of estimating the precision of the results obtained, and methods of improving the precision of results. Alternative procedures are discussed and recommendations are given.

An Improved Batch Means Procedure for Simulation Output Analysis

“…More generally, on each iteration of ASAP we use a spacer (Conway 1963, Fox et al 1991) consisting of two adjacent batches so that simulation-generated observations separated by at least one spacer are assumed to be "practically independent." If the batch size is large enough so that the batch means remaining after deletion of the initial spacer pass the test for independence or the test for multivariate normality as detailed below, then our computational experience with ASAP in a wide variety of applications has suggested that the corresponding spacer provides a reasonable warmup period (statistics clearing time) for eliminating the effects of initialization bias.…”

The random walk on the boundary method for calculating capacitance

“…To evaluate σ 2 , we use the method of batch means [20] with the number of batches, k + 1, equal to √ N + 1 and the batch size, m, equal to √ N . Thus we have…”

Perspectives on the Evolution of Simulation

“…Analysis Methodology. Richard Conway (1963) initiated a research area that became characterized as analysis methodology. This paper was the first to take a holistic approach to simulation experimentation, identifying the two phases as "strategic planning" and "tactical planning."…”

“…Removal of initial state bias (also called the initial transient problem), despite some innovative approaches, remains an unresolved problem (unless the regenerative process technique is employed). Estimation of sample variance by imposing assumptions to apply the method of replications or the batch means method (dividing one long series of output values into batches with the autocorrelation among them included in the variance estimate) are both addressed by Conway (1963). Theoretical and experimental research since that time has significantly improved the understanding of the behavioral properties of both methods.…”