两类具有N-策略和单重休假的M/G/1排队系统的最优控制策略  

Optimal control strategies for two types of M/G/1 queueing systems with N-strategy and single vacation

作　　者：唐蓓蕾 唐应辉 TANG Beilei;TANG Yinghui(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610068,Sichuan,China)

机构地区：[1]不详 [2]四川师范大学数学科学学院,四川成都610068

出　　处：《运筹学学报》2021年第4期15-30,共16页Operations Research Transactions

基　　金：国家自然科学基金(No.71571127)。

摘　　要：本文考虑两类具有N-策略和服务员单重休假的M/G/1排队系统,其中一类是休假不可中断,另一类是休假可中断。利用系统稳态队长的随机分解特性导出稳态队长的概率母函数,并讨论了系统空闲率与附加平均队长对系统一些参数的敏感性。进一步,在建立费用结构的基础上,应用更新报酬过程理论导出了系统长期运行单位时间内所产生的成本期望费用的显示表达式,同时通过数值计算实例确定了使得系统在长期运行单位时间内所产生的成本期望费用最小的控制策略N^(*),以及当休假时间为定长T时的二维最优控制策略(N^(*),T^(*))。This paper considers two types of M/G/1 queueing systems with Nstrategy and single vacation,one of which is uninterruptible on vacation and the other is of interruptible on vacation.Using the stochastic decomposition of the steady-state queue length,the expressions of the probability generating function of the steady-state queue length are obtained.And the sensitivity of the system’s idle rate and the additional average queue-length towards system parameters is discussed.Furthermore,the explicit expressions of the long-run expected cost per unit time are derived under a given cost structure.At the same time,numerical calculation examples are used to determine the control strategy N^(*)for minimizing the long-run expected cost per unit time as well as the combined control strategy(N^(*),T^(*))when the vacation time is fixed duration T.

关 键 词：N-策略 单重休假 可中断的休假 不可中断的休假 最优控制策略 

分 类 号：O226[理学—运筹学与控制论]