带有负顾客的M／M／1／N单重工作休假排队系统

研究了一个带有负顾客的M／M／1／N单重工作休假排队系统。服务员在假期中以较低的速率服务顾客而非停止工作。负顾客一对一抵消队首正在接受服务的正顾客(若有),若系统中无正顾客,到达的负顾客自动消失,负顾客不接受服务。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消失概率等性能指标。最后通过数值例子分析了系统的参数,休假时的工作率μ_v和休假率θ对平均等待队长以及顾客消失概率的影响。

The M/M/1/N queuing system with negative customers and a single working vacation

An M/M/1/N queuing system was considered with negative customers and a single working vacation.The server works at a lower rate rather than completely stops service during the vacation period.Negative customers remove positive customers only one by one at the head(if present).When a negative customer arrives,if the system is empty,it will disappear.Negative customers need no services.The matrix form solution of the steady-state probability is derived by the Markfov process method and the matrix solution met...