带有负顾客且具有反馈的M/M/1/N工作休假排队  

M/M/1/N Feedback Queue with Negative Customers and Working Vacations

作　　者：顾庆凤[1] 朱翼隽[2] 

机构地区：[1]浙江农林大学理学院,浙江临安311300 [2]江苏大学理学院,江苏镇江212013

出　　处：《数学的实践与认识》2011年第10期153-159,共7页Mathematics in Practice and Theory

基　　金：浙江省教育厅资助项目(Y201016405);浙江农林大学科研发展基金资助项目(2010FR067)

摘　　要：研究带反馈的且具有正、负两类顾客的M/M/1/N工作休假排队模型.工作休假策略为空竭服务多重工作休假.负顾客一对一抵消队首正在接受服务的正顾客(若有),若系统中无正顾客时,到达的负顾客自动消失,负顾客不接受服务.完成服务的正顾客以概率p(0<p≤1)离开系统,以概率1-p反馈到队尾寻求再次服务.利用马尔科夫过程理论和矩阵几何解方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.The paper deals with an M/M/1/N feedback queue with working vacations in which customers are either＂positive＂or＂negative＂.The working vacation policy is exhaustive service and multiple working vacations.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.Just after completion of his service,a positive customer may leave the system with probability p（0p≤1）,or feedback with probability 1-p.The matrix form solution of the steady-state probability is derived by the Markov process method and the matrix-geometric solution method.Some performance measures of the system such as the expected number of the customers in the system or in the queue and the loss probability of customers are also presented.

关 键 词：负顾客 反馈 工作休假 矩阵解 稳态概率 性能指标 

分 类 号：O226[理学—运筹学与控制论]