M/M/1/N单重工作休假排队系统的性能分析  

Performance Analysis of the M/M/1/N Queuing System with Single Working Vacation

作　　者：樊剑武[1] 赵晓华[2] 李旭红[3] 李秀菊[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 [3]中原工学院理学院,郑州450000

出　　处：《四川理工学院学报（自然科学版）》2009年第3期113-116,共4页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

摘　　要：研究了一个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。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 single working vacation. The server works at a lower rate rather than completely stops service during the vacation period. First, the matrix form solution of the 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 and in the queue and the loss probability of the customer were also presented. Finally the effect of the parameters of system were investigated, such as the vacation service rate uv 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 性能指标 矩阵解法 单重工作休假 

分 类 号：O226[理学—运筹学与控制论]