具有单重休假和Min(N,V)-策略控制的Geo/G/1离散时间排队的离去过程分析  

Analysis of the Departure Process for Geo/G/1 Discrete-Time Queue with Single Server Vacation and Min(N,V)-Policy

作　　者：兰绍军 唐应辉[1,2] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610066 [2]四川师范大学基础教学学院,成都610066

出　　处：《数学物理学报（A辑）》2016年第2期380-392,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(71171138;71571127)资助~~

摘　　要：该文研究服务员具有单重休假和系统采用Min(N,V)-策略控制的Geo/G/1离散时间排队系统的离去过程.首先,借助全概率分解方法,更新过程理论以及概率母函数技术,讨论了服务员在任意时刻点n^+处于忙的瞬态概率和稳态概率.其次,得到了在时间段(0^+,n^+]内的平均离去顾客数的概率母函数表达式.同时给出了离去过程、服务员忙的状态过程和在服务员忙期中的服务更新过程三者之间的关系,这一关系表明了系统离去过程的特殊结构.特别地,直接获得了一些特殊离散时间排队系统的离去过程的相应结果.最后,给出了便于计算任意时间段(0^+,n^+]内平均离去顾客数的渐近展式.In this paper we investigate the departure process for a Geo/G/1 discrete-time queueing system in which the server takes single server vacation and the system adopts Min（iV,Impolicy.In this study,by employing the total probability decomposition law,renewal theory and probability generating function technique,the transient and the steady probability that the server is busy at any epoch n＋ are derived.Furthermore,we also obtain the expression of the probability generating function for the expected number of departures occurring in the time interval（0＋,n＋]from any initial state.Meanwhile,the relationship among departure process,server busy-state process and the service renewal process in server busy period is found,which shows the especial structure of departure process.Especially,some corresponding results of departure process for special discrete-time queues are directly gained by the results obtained in this paper.Finally,the asymptotic expansion for calculating expected number of departures conveniently is presented.

关 键 词：离散时间排队 Min(N V)-策略 单重休假 离去过程 离去平均数 

分 类 号：O226[理学—运筹学与控制论]