具有随机检修-策略M/G/1系统队长的瞬态与稳态分析  

Transient and Steady State Analysis of M/G/1 Queueing System with Randomized Overhaul-policy

作　　者：李占宇 唐应辉 LI Zhanyu;TANG Yinghui(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：《工程数学学报》2024年第6期1155-1169,共15页Chinese Journal of Engineering Mathematics

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：研究一个具有随机检修<p,Y>-策略的M/G/1排队系统,当系统变空时,以概率p(0≤p≤1)对系统进行检修,且检修时间是具有任意分布的随机变量。首先,分析了队长的嵌入马尔可夫链,得到了其稳态分布的概率母函数。其次,讨论了在任意时刻t队长的瞬态分布,得到了队长的瞬态分布关于时间t的拉普拉斯变换表达式。在队长瞬态分析的基础上,应用洛必达法则,通过直接计算获得了在任意时刻队长的稳态分布的递推式,给出了稳态队长的随机分解结构。最后,建立了系统的费用模型,并通过数值实例得到了使系统费用最少的最优检修策略。This paper considers the M/G/1 queueing system with randomized overhaul<p,Y>-policy,in which when the system becomes empty,the system is overhauled with probability p(0≤p≤1)and the length of overhauling time is a random variable with general distribution.Firstly,we analyze the embedded Markov chain of queue length,and obtain the probability generating function of its steady-state distribution.Secondly,the transient distribution of the queue size at any time t is discussed,and the expressions of the Laplace transform of the transient queue length distribution with respect to time t are presented.Meanwhile,based on the transient analysis of the queue length,the recursive formulas of the steady-state distribution of the queue length are obtained by employing L’Hospital rule.Furthermore,the stochastic decomposition structure of the steady-state queue size is presented.Finally,numerical examples are provided to determine the optimal overhaul policy for economizing the system cost under a given cost structure.

关 键 词：M/G/1排队 随机检修 Y>-策略 全概率分解 队长分布 最优检修策略 

分 类 号：O226[理学—运筹学与控制论]