具有可变进入率和温储备失效特征的M/G/1可修排队系统  

M/G/1 Repairable Queueing System with Variable Entering Rate and Warm Standby Failure

作　　者：罗乐 唐应辉 LUO Le;TANG Ying-hui(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610068,China;Nanchong of Vocational&Technical College,Nanchong 637000,China)

机构地区：[1]四川师范大学数学科学学院,四川成都610068 [2]南充职业技术学院,四川南充637000

出　　处：《数学的实践与认识》2020年第20期82-94,共13页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71571127)。

摘　　要：考虑具有温储备失效且延迟修理的M/G/1可修排队系统,其中在温储备失效后的修理期间到达的顾客以概率p(0≤p≤1)进入系统.使用全概率分解技术和利用拉普拉斯变换工具,研究了系统从任意初始状态出发,在任意时刻t队长的瞬态分布,从而得到稳态分布.同时研究了服务台的一些可靠性指标,即服务台的不可用度、(0,t]时间内的平均失效次数及服务台温储备失效后等待修理的概率,另外,讨论了当p=0和p=1时的特殊情况.This paper considers the M/G/1 repairable queueing system with warm standby and delayed repair,in which the customers who arrive during repair period after failure of warm standby enter the system with probability p(0≤p≤1).By using the total probability decomposition technique and the Laplace transform,we discuss the transient distribution of queue length at any time t which started from an arbitrary initial state,and obtain the recursion expressions of the steady-state queue length distribution.Meanwhile,we discuss some reliability indices of the service station,such as the unavailability,the expected failure number during a given time interval(0,t]and the probability that the service station is waiting for repairing in the warm standby failure.Moreover,Some special cases are also discussed when p=1 and p=0.

关 键 词：可修排队系统 可变进入率 温储备失效 队长分布 可靠性指标 

分 类 号：O226[理学—运筹学与控制论]