IMPROVED BATCHING FOR SIMULATION OUTPUT ANALYSIS, II: ALGORITHM DEVELOPMENT

We formulate and evaluate an improved batch means procedure for steady-state simulation output analysis. The new procedure delivers a confidence interval for a steady-state expected response that is centered on the sample mean of a portion of the corresponding simulation-generated time series and satisfies a user-specified absolute or relative precision requirement. The theory supporting the new algorithm merely requires the output process to be weakly dependent (phi-mixing) so that for a sufficiently large batch size, the batch means are approximately multivariate normal but not necessarily uncorrelated. A variant of the method of nonoverlapping batch means (NOBM), the Automated Simulation Analysis Procedure (ASAP) operates as follows: the batch size is progressively increased until either (a) the batch means pass the von Neumann test for independence, and then ASAP delivers a classical NOBM confidence interval; or (b) the batch means pass the ShapiroWilk test for multivariate normality, and then ASAP delivers a corrected confidence interval. The latter correction is based on an inverted Cornish-Fisher expansion for the classical NOBM t-ratio, where the terms of the expansion are estimated via an autoregressive–moving average time series model of the batch means. An experimental performance evaluation demonstrates the advantages of ASAP versus other widely used batch means procedures.

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