中文摘要：

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．

英文摘要：

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.