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)
Replicated batch means variance estimators in the presence of an initial transient
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Simulation Modeling and Analysis (McGraw-Hill Series in Industrial Engineering and Management)
Simulation Modeling and Analysis (McGraw-Hill Series in Industrial Engineering and Management)
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
Analysis of initial transient deletion for replicated steady-state simulations
Operations Research Letters
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The replicated batch means RBM method for steady-state simulation output analysis generalizes both the independent replications IR and batch means BM methods. We analyze the performance of RBM in situations where the underlying stochastic process possesses an additive initial transient. Our analysis differs from prior work in that the initial transient is stochastic, and hence the sample paths of the transient process may be replication dependent, and possibly also correlated across replications. We provide asymptotic expressions for the mean and variance of the RBM estimators of the steady-state mean and variance parameter of the stochastic process being simulated. We then use our results to study the performance of RBM as a function of the number of replications, initialization method for the replications, and decay rate of the associated initialization bias. Our results provide guidance on when IR, BM, or a combination thereof is the best choice, and also on effective choices of initial states for the replications.