研究了具有插队行为和服务员单重休假的有限容量$M/M/1/m+1$排队系统中顾客的等待时间分布函数。将进入系统的顾客按照插队与否分为常规顾客和插队顾客，常规顾客进入系统后在等待队尾排队等待服务，插队顾客进入系统后总是尽可能的靠近队首插队接受服务。系统中有一个服务员，且采取单重休假策略。利用负指数分布、位相型分布的性质、吸收时间的马尔可夫链推导了处于等待队列位置$n$的顾客、常规顾客、插队顾客的等待时间分布函数的矩阵表达式，并在此基础上数值模拟了等待时间分布函数随时间的变化情况。

This paper studies the waiting time distributions of customers in an $M/M/1/m+1$ queueing system with customer interjections and server's single vacation. The customers who enter the system are divided into regular customers and interjection customers according to whether they interject the queue or not. After entering the system, the regular customers queue up at the end of the waiting line and wait for service, while the interjection customers queue up as close as possible to the head of the waiting line to receive service. There is one server who takes single vacation in the system. By using the properties of negative exponential distribution, the phase type distribution and the Markov chain with absorbing state, the matrix expressions of waiting time distribution of customers in waiting queue position $n$, regular customers and interjection customers are derived. Further, the waiting time distributions with time $t$ are plotted.