带有负顾客的M/M/1/N单重工作休假排队系统  

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

作　　者：樊剑武[1] 赵晓华[2] 田乃硕[2] 贠小青[1] 

机构地区：[1]燕山大学里仁学院,河北秦皇岛066004 [2]燕山大学理学院,河北秦皇岛066004

出　　处：《山东大学学报（理学版）》2009年第8期68-73,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10671170)

摘　　要：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μv和休假率θ对平均等待队长以及顾客消失概率的影响。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 method. Some performance measures of the system such as the expected number of customers the system or in the queue and the loss probability of the customer are also presented. Finally the effects of the parameters of the system are investigated, such as the vacation service rate ,μv and the vacation rate θ on the expected waiting queue length and the loss probability of customers by numerical examples.

关 键 词：排队系统 稳态概率 矩阵解法 负顾客 单重工作休假 

分 类 号：O226[理学—运筹学与控制论]