带有止步和中途退出的M/M/1/N多重休假排队系统的等待时间

The Waiting Time of the M/M/1/N Queuing System with Balking Reneging and Multiple Vacations

本文研究了带有止步和中途退出的多重休假排队系统模型,该排队模型的稳态概率已在我们的另一篇文章中给出。本文的目的是在稳态概率的基础上推导系统的稳态等待时间分布。通过对进入系统的顾客可能中途退出的不同情况的概率分析,我们分别在服务员忙和休假的情况下得到了进入系统并接受服务的顾客的稳态条件等待时间分布,进而得到了进入系统并接受服务的顾客的稳态条件等待时间的概率密度。

In this paper, we study a queuing system model with balking, reneging and multiple vacations. The steady state probability for this queuing model has been obtained in our previous paper. The purpose of this paper is to derive the probability distribution of the steady state waiting time based on the steady state probability. By introducing different probability analyses for the different cases that the customers in the system may renege, we obtain the distribution of the steady state waiting time of the customers that enter the system and acquire the service under the condition that the server is busy and on vacation, respectively. Then, we obtain the probability density of the steady state condition waiting time of the customers that enter the system and acquire the service.