【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.更多还原

【Abstract】 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.更多还原