Queueing Simulation in Heavy Traffic
研究了样本平均和再生模拟等标准排队模拟方法在高负荷下的行为，给出了基于布朗近似的双重极限定理，发现样本量需按(1-ρ)^{-2}增长，且负偏差是严重问题。
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.