带有止步和中途退出的M/M/c/N排队系统分析——部分不可靠服务器模型  

Analysis of M/M/c/N Queuing System with Balking and Reneging——Partial Unreliable Servers

作　　者：李海英[1] 岳德权[1] 王玲[1] 许厅厅[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《运筹与管理》2010年第2期72-78,共7页Operations Research and Management Science

基　　金：国家自然科学基金项目资助(70671088)

摘　　要：本文研究了带有止步和中途退出的部分服务器不可靠的M/M/c/N的排队系统,其中到达的顾客若看到系统中等待的顾客过多则可能不进入系统,而进入队列中的顾客也可能因为等待的不耐烦而没有接受服务就离开系统。首先,利用马尔可夫过程理论建立了系统稳态概率方程组。其次,利用分块矩阵的解法求出系统稳态概率的矩阵解,并得到了系统的平均队长、平均等待队长及顾客的平均中途离去率等性能指标。最后,同时利用M atlab软件进行了数值分析。In this paper, we consider M/M/C/N queuing system with balking, reneging and partial unreliable servers. In this system, if arriving customers find that there are too many customers in the system then they may not enter system, while the entering customers may leave without being serviced because of impatience of waiting. Firstly, we obtain the steady-state probability equations by the Markov process method. Secondly, we derive the steady-state probability in matric form by block matric solution theory. Some performance measures of the system such as the expected number of customers in the system, the expected number of customers in the queue and the average reneging rate of the customer are presented. Finally, we make numerical analysis by using Matlab software.

关 键 词：排队系统 马尔可夫过程 止步 中途退出 平均队长 

分 类 号：O226[理学—运筹学与控制论]