A comparison of output-analysis methods for simulations of processes with multiple regeneration sequences

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.