Optimal mean-squared-error batch sizes
Management Science
Large-sample results for batch means
Management Science
Discrete-event simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A comprehensive review of methods for simulation output analysis
Proceedings of the 38th conference on Winter simulation
Statistical analysis of simulation output: state of the art
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Replicated batch means for steady-state simulations with initial transients
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Steady-State Simulation with Replication-Dependent Initial Transients: Analysis and Examples
INFORMS Journal on Computing
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Independent replications (IR) and batch means (BM) are two of the most widely used variance-estimation methods for simulation output analysis. Alexopoulos and Goldsman conducted a thorough examination of IR and BM; and Andradóttir and Argon proposed the method of replicated batch means (RBM), which combines good characteristics of IR and BM. This article gives analy-tical results for the mean and variance of the RBM estimator for a class of processes having initial transients with an additive form. Along the way, we provide succinct complementary extensions of some of the results in the aforementioned papers. Our expressions explicitly show how the transient function affects estimator performance and suggest that in some cases, the RBM estimator is a good compromise choice with respect to bias and variance. However, care must be taken to avoid an excessive number of replications when the transient function is pervasive. An example involving a simple moving average process illustrates our findings.