To batch or not to batch?

Abstract

When designing steady-state computer simulation experiments, one may be faced with the choice of batching observations in one long run or replicating a number of smaller runs. Both methods are potentially useful in the course of undertaking simulation output analysis. The tradeoffs between the two alternatives are well known: batching ameliorates the effects of initialization bias, but produces batch means that might be correlated; replication yields independent sample means, but may suffer from initialization bias at the beginning of each of the runs. We present several new results and specific examples to lend insight as to when one method might be preferred over the other. In steady-state, batching and replication perform similarly in terms of estimating the mean and variance parameter, but replication tends to do better than batching with regard to the performance of confidence intervals for the mean. Such a victory for replication may be hollow, for in the presence of an initial transient, batching often performs better than replication when it comes to point and confidence-interval estimation of the steady-state mean. We conclude-like other classic references-that in the context of estimation of the steady-state mean, batching is typically the wiser approach.

Performance evaluation of recent procedures for steady-state simulation analysis

“…, k} are approximately independent and identically distributed (i.i.d.) normal random Lada et al variables with mean µ X , then we can apply classical results concerning Student's t-distribution (see, for example, Alexopoulos and Goldsman (2004)) to compute a CI for µ X from the batch means. For this purpose we compute the sample variance of the k batch means for batches of size m,…”

SimQPN—A tool and methodology for analyzing queueing Petri net models by means of simulation

“…Different approaches have been proposed in the literature to address this problem (see for example [11,1,33]). In SimQPN, we start with a userconfigurable initial batch size (by default 200) and then increase it sequentially until the correlation between successive batch means becomes negligible.…”

“…Most methods attempt to estimate the length of the warm-up period and then discard all data collected during it to eliminate initialization bias. One of the simplest and most popular methods is the graphical method of Welch [44,16], which has met some success [26,1]. The latter is appealing because it is simple, practical and does not make any assumptions about the type of system modeled.…”

SPSTS: A sequential procedure for estimating the steady-state mean using standardized time series

“…ACCEPTED MANUSCRIPT see Alexopoulos and Goldsman (2004). If both m and b tend to ∞, then the last two equations imply weak…”