Using permutations in regenerative simulations to reduce variance
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on modeling and analysis of stochastic systems
SIMULATION OF PROCESSES WITH MULTIPLE REGENERATION SEQUENCES
Probability in the Engineering and Informational Sciences
The semi-regenerative method of simulation output analysis
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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We compare several simulation estimators for a performance measure of a process having multiple regeneration sequences. We examine the setting of two regeneration sequences. We compare two existing estimators, the permuted estimator and the semi-regenerative estimator, and two new estimators, a type of U -statistic estimator and a type of V -statistic estimator. The last two estimators are obtained by resampling trajectories without and with replacement, respectively. The permuted estimator and the U -statistic estimator turn out to be equivalent, but the others are in general different. We show that when estimating the second moment of a cumulative cycle reward, the semi-regenerative and V-statistic estimators have non-negative bias, with the semi-regenerative bias being larger. The permuted estimator was previously shown to be unbiased. Although some of the estimators have different small-sample properties, they all satisfy central limit theorems with the same asymptotic variance constant.