带有故障的休假排队模型

A Vacation Queueing Model with Breakdowns

研究了一个复合的休假排队模型,工作或休假时服务台都有可能故障,服务台一旦修好可立即进行服务,而且每个忙期结束就开始一次休假,顾客到达服从Poisson过程,到达率依赖于系统状态,修理时间、服务时间和休假长度都服从指数分布.给出了系统状态的平衡方程,利用概率母函数求出队长,并做了数值分析.

In this paper we consider a multiple-vacation queueing model, where the service station is subject to breakdown while in operation or on vacation .Service resumes immediately after a repair process, and a vacation starts at the end of each busy period. Arrivals follow a Poisson process with rates depending upon the system state. The repair time ,uninterrupted service time and length of each vacation follow exponential distributions. Give a balance equation of describing the system state, and obtain the mean queue length by using the generating function. Finally we give some numerical analysis.