Queueing Simulation in Heavy Traffic

The heavy traffic behavior of a number of standard queueing simulation procedures like sample averaging and regenerative simulation is studied. In particular, limit theorems based upon Brownian approximations are given in a double limit with both the sample size t tending to infinity and the traffic intensity ρ tending to one. The results demonstrate that the growth rate t = t(ρ) ≈ (1 − ρ)⁻² plays a critical role, and it follows both from the present theoretical results and empirical illustrations in a companion paper that negative bias presents a serious problem. Furthermore the heavy traffic behavior of the limiting variances in the standard large sample theory is found.