具有检修策略和顾客进入控制策略的排队系统分析  

Analysis of a Queueing System with Admission Control and Overhaul Policy

作　　者：柯淇淋 唐应辉 余玅妙 KE Qilin;TANG Yinghui;YU Miaomiao(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610068)

机构地区：[1]四川师范大学数学科学学院,成都610068

出　　处：《系统科学与数学》2023年第8期2164-2181,共18页Journal of Systems Science and Mathematical Sciences

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

摘　　要：考虑有检修策略和顾客进入控制策略的M/G/1排队系统,其中在系统检修期内至多允许M(≥1)个顾客进入系统.应用更新过程理论、全概率分解方法和拉普拉斯变换工具,讨论了系统在任意初始状态下队长在时刻t的瞬态分布,得到了瞬态队长分布关于时间t的拉普拉斯变换表示式,然后使用洛必达法则,获得了稳态队长分布的递推表达式.进一步讨论了当M→∞及P{Y=0}=1的特殊情形.最后,应用更新报酬定理求得了系统长期运行下单位时间内的期望费用函数,并通过数值算例求得了使费用最小的最优控制策略M*,以及当检修时间为固定时长T时的二维最优控制策略(T*,M*).This paper considers an M/G/1 queueing system with admission control and overhaul policy,in which at most M(≥1)customers are allowed to enter the system during system's overhaul period.Under any initial state,we employ the renewal process theory,total probability decomposition technique and Laplace transform to discuss the transient queue length distribution of the system,and obtain the expressions of the Laplace transform of the transient queue length distribution with respect to time t.Then,the recursive formulas of the steady-state queue-length distribution are obtained by using L'Hospital's rule.Moreover,some special cases such as M→∞and P{Y=0}=1 are also discussed.At last,applying the renewal reward theory,the explicit expression of the long-run expected cost per unit time is presented,and numerical examples are provided to determine the optimal control policy M*for economizing the system cost as well as the optimal two-dimensional control policy(T*,M*)when the overhaul time is a fixed length T.

关 键 词：M/G/1排队 检修策略 进入控制策略 全概率分解 队长分布 

分 类 号：O226[理学—运筹学与控制论]