有启动失败和负顾客的M^X/G/1重试排队模型  

An M^X/G/1 Retrial Queue with Starting Failures and Negative Customers

作　　者：高珊[1,2] 刘再明[2] 

机构地区：[1]阜阳师范学院数学与计算科学学院,安徽阜阳236032 [2]中南大学数学科学与计算技术学院,湖南长沙410075

出　　处：《系统工程》2011年第9期98-104,共7页Systems Engineering

基　　金：国家自然科学基金资助项目(10971230)

摘　　要：研究有负顾客到达的MX/G/1重试排队模型,其中服务台有可能启动失败。负顾客在服务台忙时以到达率为δ的Po isson流进入系统,且以概率θ(0<θ≤1)带走正在服务的正顾客,否则以概率1-θ正顾客继续接受服务。通过嵌入马尔可夫链法给出了系统稳态的充要条件并给出了嵌入马尔可夫链的稳态分布。利用补充变量法得到了稳态时系统和重试区域中队长以及系统的各种指标,并给出了系统队长的随机分解性和几种特例,最后给出了几个数值例子来说明各参数对一些系统性能指标的影响。An MX/G/1 retrial queue with negative customers and starting failures is considered.Negative customers arrive according to a Poisson process with parameter δ when the positive customer is undergoing service,and a positive customer undergoing service gets annihilated with probability θ（0θ≤1） or survives the onslaught of an arriving negative customer with probability 1-θ and continues his service.By using embedded Markov chain,the necessary and sufficient condition for the system stability is derived and the stationary distribution of the embedded Markov chain is given.The steady-state distributions of the number of customers in the system and orbit and other performance measures are obtained through method of supplementary variables,and the stochastic decomposition property and some special cases are analyzed.At last some numerical examples are given to illustrate the impact of the parameters on the some performance characteristics.

关 键 词：重试排队 启动失败 负顾客 稳态队长 随机分解 

分 类 号：O266[理学—数学]