On Poisson Approximations for Superposition Arrival Processes in Queues
通过模拟多达1024个独立同分布更新过程的叠加到达队列，发现随着到达过程数量增加，系统平均顾客数趋近M/M/1队列，但差值随流量强度增大而显著增加，并给出了近似公式。
We report on simulations of Σ i GI i /M/1 queues; the arrival process is the superposition (sum) of up to 1024 i.i.d. renewal processes and there is a single exponential server. As one might anticipate, the simulation estimate of the expected number of customers in a Σ i GI i /M/1 queueing system approaches the expected number in an M/M/1 queueing system as the number of arrival processes, n, increases. However, for a given n, the difference between the expected numbers in the M/M/1 and Σ i GI i /M/1 queueing systems dramatically increases as the traffic intensity increases from ρ = 0.5 to ρ = 0.9. This difference is approximated by a formula which is a function of the traffic intensity, the number of component arrival processes and the squared coefficient of variation of the component interarrival times.