M/M/1/N多重工作休假排队系统的性能分析  

Performance Analysis of M/M/1/N Queuing System with Multiple Working Vacations

作　　者：赵晓华[1] 樊剑武[2] 田乃硕[1] 田瑞玲[1] 

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

出　　处：《运筹与管理》2009年第4期54-59,共6页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(10671170)

摘　　要：本文研究M/M/1/N多重工作休假排队系统,简记为M/M/1/N(WV)。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。最后通过数值例子我们分析了系统的参数,休假时的工作率μν和休假率θ对平均队长的影响。In this paper, we consider an M/M/1/N queuing system with multiple working vacations, and we have M/M/1/N （WV） in short. First, we derive the matrix form solution of the steady-state probability 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 loss probability of the customer are also presented. Finally we investigate the effect of the parameters of system, such as the vacation service rate and the vacation rate on the expected queue length by numerical examples.

关 键 词：排队系统 稳态概率 性能指标 马尔科夫过程 矩阵解法 多重工作休假 

分 类 号：O226[理学—运筹学与控制论]