We show that there is no batch-means estimation procedure for consistently estimating the asymptotic variance when the number of batches is held fixed as the run length increases. This result suggests that the number of batches should increase as the run length increases for sequential stopping

is the variance parameter, i.e., the limiting value of the sample size multiplied by the variance of the sample mean as n becomes large. This paper establishes asymptotic properties of the conventional batch-means (BM) estimator of the variance parameter as both the batch size and the number of batches become

This paper reviews and evaluates strategies for implementing the batch means method for estimating the mean of a stationary simulation output process. 1

Nonoverlapping batch means (NOLBM) is a a we11-known approach For For estimating the variance of the sample mean. In this paper we consider an overlapping batch means (OLBM) estimator that, based on the same assumptions and batch size as as NOLBM, has has essentially the same mean and only 2

Thisarticlediscussesimplementationissuesforthe LBATCHandABATCHbatchmeansproceduresof FishmanandYarberry(1997).Thesesproceduresdynamicallyincreasethebatchsizeandthenumberof contiguousbatchesbasedontheoutcomeofahypothesistestforindependenceamongthebatchmeans. WeshowthatbothproceduresrequireO(n)time andO(log 2 n)space,wherenisthedesiredsample size.Althoughlikecomplexitiesareknownforstatic fixedbatchsizealgorithms,thedynamicsettingofthe LBATCHandABATCHruleso#ersanimportantadditionaladvantagenotpresentinthestaticapproach. Astheanalysisevolveswithincreasingsamplepath length,itallowsausertoassesshowwelltheestimatedvarianceofthesamplemeanstabilizes. This assessmentisessentialtogaugethequalityofthe confidenceintervalforthesamplemean.TheLABATCHimplementation (describedinFishman1996 andFishmanandYarberry1997)oftheLBATCH andABATCHrulesistheonlycomputerpackagethat automaticallygeneratesthedataforthisassessment. 1

algorithm for steady-state simulation output analysis based on the method of nonoverlapping batch means (NOBM). ASAP delivers a confidence interval for an expected response that is centered on the sample mean of a portion of a simulation-generated time series and satisfies a user-specified absolute

this paper is organized as follows. Section 2 contains an overview of the operation of ASAP. Section 3 documents the statistical methods used by ASAP to test a sequence of batch means separately for independence and multivariate normality. In Section 4 we describe howASAP builds a time series model

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 datacollection methods, despite its

to the application of data-reuse techniques designed to improve estimator accuracy and efficiency. Many of the key insights regarding data reuse are given in the seminal 1984 Winter Simulation Conference paper by Meketon and Schmeiser that is titled “Overlapping Batch Means: Something for Nothing

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