Validating the heavy traffic performance of regenerative simulation

Following a theoretical study by Asmussen indicating severe problems associated with a number of standard queueing simulation schemes in heavy traffic situations, the paper looks into one of the possible settings of regenerative simulation from a more empirical point of view. Sequences of queues with ρ↑1 are simulated subject to various growth rates t=t(ρ) of the sample size t, the empirical distribution of a certain Brownian functional describing the heavy traffic limit of the regenerative estimator is exhibited and compared to that of the estimator itself, and finally similar experiments are performed for the regenerative variance estimator.