带有止步和中途退出的M／M／1／N多重工作休假排队系统

研究了一个带有止步和中途退出的M／M／1／N多重工作休假排队系统。利用马尔科夫过程理论和矩阵解法求出了稳态概率的矩阵解,并得到了系统的平均队长、平均等待队长以及顾客的平均损失率等性能指标。最后通过数值例子分析了系统的参数,休假时的工作率μv和休假率θ对平均队长的影响。

The M/M/1/N queuing system with balking, reneging and multiple working vacations

An M／M／1／N queuing system was considered with balking, reneging and multiple working vacations. First, the matrix form solution of steady-state probability was derived by the Markfov process method and the matrix solution method. Some performance measures of the system such as the expected number of customers in the system or in the queue and the average rate of the customer loss were also presented. Finally, the effect of the parameters of the system were investigated by numerical examples, such as the vacation service rate μv and the vacation rate θ on the expected queue length.