有Bernoulli检修与顾客进入控制策略的M/G/1可修排队的可靠性  

Reliability of M/G/1 Repairable Queue with Bernoulli Maintenance and Admission Control Strategy

作　　者：刘雨欣 唐应辉 魏瑛源 LIU Yuxin;TANG Yinghui;WEI Yingyuan(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610068,China;School of Mathematics and Statistics,Hexi University,Zhangye 734000,China)

机构地区：[1]四川师范大学数学科学学院,四川成都610068 [2]河西学院数学与统计学院,甘肃张掖734000

出　　处：《应用数学》2024年第3期672-683,共12页Mathematica Applicata

基　　金：国家自然科学基金(71571127);四川师范大学学科建设专项项目基金(XKZX2021-04);河西学院校长基金创新团队项目(CXTD2022013)。

摘　　要：本文研究一个具有Bernoulli检修与顾客进入控制策略的M/G/1可修排队模型,其中服务台在服务顾客期间可能发生故障.Bernoulli检修与顾客进入控制策略是指每当系统变空时依概率p(0≤p≤1)进入检修,或者依概率(1−p)不进入检修而是等待下一个顾客进入系统后直接开始服务,而且在系统的检修期内至多允许N个顾客进入.运用更新过程理论、全概率分解技术与拉普拉斯变换工具,我们对系统的一些可靠性指标进行了讨论,例如时刻t服务台处于故障状态的概率、在(0,t]内服务台的平均失效次数等等.最后通过数值计算研究了一些系统参数对系统可靠性指标的影响.In this paper,we study an M/G/1 repairable queueing model with Bernoulli maintenance and admission control policy,in which the service station may be subject to breakdowns during the period of serving customers.The Bernoulli maintenance and admission control strategy means that whenever the system becomes empty,the manager shuts down the system immediately with probability p(0≤p≤1)and arranges the repairman to maintenance it where at most N(≥1)customers are allowed to enter into the system during its maintenance period,or the manager don’t shut down the system with probability 1−p until next customer enter the system and start its service at once.Using the renewal process theory,total probability decomposition and Laplace transform tool,a series of reliability indices of the system,such as the probability of the service station being in a failed state at time t,the expected failure number of the service station during(0,t]and so on,are discussed.Finally,several numerical examples are presented to investigate the effects of some system parameters on reliability performance measures of the system.

关 键 词：M/G/1可修排队 Bernoulli检修策略 顾客进入控制策略 全概率分解 可靠性指标 

分 类 号：O213.2[理学—概率论与数理统计]