两类具有N-策略和多重休假的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-Policy and Multiple Vacations

作　　者：唐蓓蕾 唐应辉 高文萍 TANG Bei-lei;TANG Ying-hui;GAO Wen-ping(School of Mathematical Sciences,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

出　　处：《数学的实践与认识》2023年第7期120-129,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71571127);四川师范大学学科建设专项基金(XKZX2021-04)。

摘　　要：考虑两类具有N-策略和服务员多重休假的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的.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,用数值计算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,在给出的费用结构模型的基础上,利用更新报酬定理,推导出了稳态下系统在单位时间内的数学期望平均费用目标函数的解析式,然后借用MATLAB软件,求出了使目标函数达到最小的最优控制策略N*.This paper considers two types of M/G/1 queueing systems with N-policy and multiple sever vacations,one of which is uninterruptible vacation and the other is of interruptible vacation.Utilizing the random decomposition property of the steady-state queue size,we give the expressions of the probability generating function of the steady-state queue length.By numerical examples,we discuss the sensitivity of the idle rate and the additional average queue length towards system parameters.Furthermore,the expressions of the longrun expected cost per unit time are derived under a given cost structure.Simultaneously,using MATLAB to do numerical calculations,the control strategy N*,which minimizes the long-run expected cost of the system per unit time,is acquired.

关 键 词：N-策略 多重休假 可中断休假 不可中断休假 最优控制策略 

分 类 号：O226[理学—运筹学与控制论] O232[理学—数学]