一类具有可变输入率的M/M/1排队模型

A M/M/1 Queuing Model with Variable Input Rate

讨论了到达的顾客以概率α_k=1/(βk+1)进入M/M/1排队系统的可变输入率模型,获得了该模型的平稳分布和顾客的平均输入率,系统的平均服务强度,平均等待队长,系统的平均队长,系统的损失概率,顾客进入系统并接受服务的概率,单位时间内平均进入系统的顾客数,单位时间内平均损失的顾客数等相关指标,从而推广了文献[1]中的结果。

The M/M/1 queuing theory of variable input rate is an important queuing model. Customers are frequently seen in our daily life hesitating about joining the long queue when they find so many people waiting in the line in front of the service desk. Generally speaking, the probability for customers joining the queue changes with the length of it. This paper, by discussing the M/M/1 queuing model when the customers arrived entering this queuing system by the probability of αk=1/βk＋1 aims at getting the stable distribution and the related indexes of this modals, such as the average input rate of customers, the average intensity of the service of the system, the average number of the customers, the average number of the customers of the system, the loss probability of the system, the probability of customers getting into the system and receiving service, the average number of customers getting into the system in a given time, the average number of customers lost in a given time ect. Thus it extends the application of the results in reference [ 1 ].