输入率可变且有差错服务的M/M/1排队系统的研究与应用

在到达系统的顾客数不变的情况下,顾客到达系统但是否进入系统接受服务对销售行业影响是巨大的.从排队长度对顾客输入率的影响着手,研究了顾客以泊松流到达系统,而到达系统的顾客进入系统接受服务的概率与队长有关的M/M/1排队模型,且系统服务会出差错.得出了进入系统的顾客流是泊松过程,且系统中的顾客数是生灭过程,并获得了该模型的平稳分布、顾客的平均输入率、系统的平均服务强度等多项指标,为销售行业调整自己的服务速度以影响排队长度及顾客输入率,进而提高自己的销售业绩提供了很有价值的参考.

The Rsearch and Aplication of M/M/1 Queuing Model with Variable Input Rates

The customers do not necessarily get into the system though arriving at the system in the case of the number of customers is fixed,which influences sales enormous.This paper researches the influence of queue length to input rate,and sets up a kind of M/M/1 queuing model as such: the customers reach system at Poisson flow.But they do not necessarily get into the system though arriving at the system.While the probability they getting into the system is connected with the queue length,and the system works wrongly some time.This paper draws a conclusion that the number of customers who getting into the system is a Poisson flow,and the number of customers in the system is a birth-and-death process,also draws that the stationary distribution of this model、the average customer arrival rate、the average intensity of the system and so on,which provides a valuable reference for the retail industry to adjust their service speeds in order to influence the rate of queue length and customer input,and thus improve their sales performance.