Approximations for Superposition Arrival Processes in Queues
解释了S. L. Albin关于单服务器排队系统叠加到达过程的仿真结果,指出当流量强度接近1时,系统趋近M/M/1的速度变慢,且需要满足n(1-ρ)^2远大于1的条件。
S. L. Albin has described extensive simulations of queue behavior for a system with a single server and an arrival process that is a superposition of n renewal processes. The simulations show, among other things, that as n increases for a fixed traffic intensity ρ, the queue behavior approaches that of the M/M/1 system. The rate of convergence, however, becomes much slower as the traffic intensity ρ comes closer to 1. Several qualitative effects shown in the simulations are explained here. In particular it is shown that the approach to the M/M/1 system requires that n(1 − ρ) 2 ≫ 1.