ASAP3: a batch means procedure for steady-state simulation analysis

  • Authors:

  • Natalie M. Steiger;Emily K. Lada;James R. Wilson;Jeffrey A. Joines;Christos Alexopoulos;David Goldsman

  • Affiliations:

  • University of Maine, Orona, ME;Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, NC;North Carolina State University, Raleigh, NC;North Carolina State University, Raleigh, NC;Georgia Institute of Technology, Atlanta, GA;Georgia Institute of Technology, Atlanta, GA

  • Venue:
  • ACM Transactions on Modeling and Computer Simulation (TOMACS)
  • Year:
  • 2005

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Abstract

We introduce ASAP3, a refinement of the batch means algorithms ASAP and ASAP2, that delivers point and confidence-interval estimators for the expected response of a steady-state simulation. ASAP3 is a sequential procedure designed to produce a confidence-interval estimator that satisfies user-specified requirements on absolute or relative precision as well as coverage probability. ASAP3 operates as follows: the batch size is progressively increased until the batch means pass the Shapiro-Wilk test for multivariate normality; and then ASAP3 fits a first-order autoregressive (AR(1)) time series model to the batch means. If necessary, the batch size is further increased until the autoregressive parameter in the AR(1) model does not significantly exceed 0.8. Next, ASAP3 computes the terms of an inverse Cornish-Fisher expansion for the classical batch means t-ratio based on the AR(1) parameter estimates; and finally ASAP3 delivers a correlation-adjusted confidence interval based on this expansion. Regarding not only conformance to the precision and coverage-probability requirements but also the mean and variance of the half-length of the delivered confidence interval, ASAP3 compared favorably to other batch means procedures (namely, ABATCH, ASAP, ASAP2, and LBATCH) in an extensive experimental performance evaluation.