具有Bernoulli休假和负顾客到达的Geo/G/1早到达重试排队系统  

Geo/G/1 Early Arrival Retrial Queueing System with Negative Customers and Bernoulli Vacation

作　　者：薛红 唐应辉 XUE Hong;TANG Ying-hui(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610068,China;School of Fundamental Education,Sichuan Normal University,Chengdu 610068,China)

机构地区：[1]四川师范大学数学科学学院,四川成都610068 [2]四川师范大学基础教学学院,四川成都610068

出　　处：《数学的实践与认识》2021年第12期111-119,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71571127)。

摘　　要：考虑一个有Bernoulli休假和负顾客到达的离散时间Geo/G/1早到达重试排队系统,其中在服务台前无等待位置,顾客若发现服务台忙或处于休假,则进入重试轨道等待服务,若服务台空闲则立即接受服务.假设负顾客抵消正在接受服务的正顾客,服务台每完成一次服务,以概率η(0 ≤η≤ 1)进行一次休假,以概率η=1-η对下一个顾客进行服务.利用马尔可夫链法和补充变量法推导出了系统演化的平衡方程组,从而得到了嵌入马氏链的平稳分布和一系列排队指标.最后通过数值实例讨论了一些参数对系统性能的影响.We consider a Geo/G/1 retrial queue with negative customers where the retrial time has a general distribution and the server is subject to Bernoulli vacation policy.There is no waiting position in the server,and a new arriving customer finds the server is busy or at vacation,he will join the orbit to retry getting the service,if the server is free,he will accept service at once.It is assumed that negative customers offset the customers of receiving the service.The server after each service completion begins a single vacation with probabilityη(0≤η≤1) or begins to another service with probability η=1-η.Employing the supplementary variable method and the generating function,the equilibrium equations of the evolution of the system are derived,and the stationary distribution of the embedded Markov chains and a series of queueing indices are obtained.Finally some numerical examples are provided to illustrate the impact of several parameters on some performance characteristics of the system.

关 键 词：重试排队 负顾客 BERNOULLI休假 补充变量法 母函数 

分 类 号：O226[理学—运筹学与控制论]