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中文摘要：
研究了带有止步和中途退出的M／M／R／N部分服务员同步单重休假的排队系统．假定在服务员全忙时，到达的顾客以一定的概率不进入系统，而进入系统的顾客可能因为等待得不耐烦则中途退出系统．当某顾客离去使得系统中的顾客数减少到定值R—d（1≤d〈R）时，空出的d个服务员立即进行同步单重休假．利用马尔可夫过程理论，建立了系统稳态概率方程组，用分块矩阵解法，得到了稳态概率的矩阵解，并求出了系统的性能指标．在此基础上，建立了系统费用模型，并通过数值方法进行了敏感性分析．
英文摘要：
An M/M/R/N queue with balking , reneging and single synchronous vacation of partial servers was examined in this paper. It is assumed that a new arrival may balk （without entering the system） with a certain probability when the servers are all busy, while the joining customers may leave the system without acquiring service （reneging） because of impatient waiting. When a customer leave makes the number of the customers in the system reduce to a constant R-d （1 ≤ d 〈 R）, the idle d servers immediately take single synchronous vacation. Using Markov process method, authors created the steady state probability equations. Employing block matrix solution method, the matrix form solution of the steady-state probability and some performance measures of the system were obtained. A cost model of the system and sensitivity analysis by numerical method were developed based on the performance measures.
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