部分服务时间不独立的D策略和单重休假M/G/1排队  

The D-Policy and Single Vacation M/G/1 Queue with Part Service Times Being Dependent

作　　者：刘仁彬 唐应辉[2] LIU Renbin;TANG Yinghui(School of Science,Chongqing University of Technology,Chongqing 400054;School of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066)

机构地区：[1]重庆理工大学理学院,重庆400054 [2]四川师范大学数学与软件科学学院,成都610066

出　　处：《系统科学与数学》2023年第1期94-113,共20页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(71571127);重庆市自然科学基金面上项目(CSTB2022NSCQ-MSX1160)资助课题。

摘　　要：在已有的控制排队文献基础上,文章考虑了一个D策略和单重休假的M/G/1排队,其中服务员闲期到达顾客的服务时间是不独立的,而服务员忙期到达顾客的服务时间是相互独立的.由于服务时间的不同特点,因此稳态队长的随机分解规律不再成立.通过定义服务员闲期和忙期、并将顾客分成两类以及借助拉普拉斯变换和概率分析,研究了该排队系统的一些稳态性能指标分布,如服务员闲期、忙期、忙期开始时的队长和服务时间积压量以及任意时刻的服务时间积压量和队长等.最后,通过获得两个特殊排队的稳态平均性能指标和数值分析,进一步说明了文章理论分析的正确性.文章的研究结果表明,部分服务时间不独立的D策略和单重休假M/G/1排队和已有文献的研究具有完全不同的排队指标结果。On the basis of the existing control queueing references,a D-policy and single vacation M/G/1 queue is considered,in which the service times of the customers who arrive during server idle period are dependent while the service times of the costumers who arrive during server busy period are mutually independent.Due to different characteristics of the service times,the stochastic decomposition law for the steady-state queue length does not hold.By the definitions of server idle and busy periods,two categories of the customers,Laplace transform and probabilistic analysis,the steady-state distributions of some performance indices are researched,such as the idle and busy periods,queue length and service time backlog at the start of server busy period,and queue length and service time backlog at an arbitrary time,etc.Finally,by the steady-state mean performance indices for two special queues,and a numerical analysis,the correctness of theoretical analysis is further showed.The research results in this paper show that there are totally different queueing performance indices between the D-policy and single vacation queue with part service times being dependent,and the existing research reference.

关 键 词：D策略 休假 M/G/1排队 服务时间积压量 队长 

分 类 号：O226[理学—运筹学与控制论]