假期中以概率p进入的单重休假M/G/1排队系统的控制策略  

Control Policy of M/G/1 Queueing System with p-Entering Discipline During Single Server Vacation

作　　者：钟瑶 唐应辉 ZHONG Yao;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》2022年第11期247-255,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71571127)。

摘　　要：考虑在-策略控制下服务员具有单重休假的M/G/1排队系统,其中在服务员休假期间到达顾客以概率p(0≤p≤1)进入系统.在建立费用结构模型的基础上,使用更新报酬定理,推导出了系统长期单位时间内的期望费用的显示表达式,然后在服务员休假时间内顾客进入概率p固定不变的情况下,通过数值实例讨论了服务员休假时间的最优控制策略T^(*).进一步,从系统服务能力的角度,讨论了在限制平均队长不超过某个固定正整数阈值L0条件下允许进入概率p的最佳取值p^(*).This paper considers the M/G/1 queueing system with-control policy and single server vacation in which the customers who arrive during server vacation enter the system with probability p(0≤p≤1).Under a given cost structure,by using renewal reward theorem,the explicit expression of the long-run expected cost per unit time is derived.When the entering probability p that the customers who arrive during server vacation time enter the system is fixed,we numerically determine the optimum control policy T^(*)for minimizing the long-run expected cost per unit time.Furthermore,from system service capability perspective,the optimum value p^(*)for the probability p allowed into the system is also discussed numerically under the expected queue size no more than a fixed positive integer threshold L0.

关 键 词：p-进入规则 M/G/1排队 单重休假 费用期望 最优控制策略 

分 类 号：O226[理学—运筹学与控制论]