【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.更多还原

【Abstract】 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 probability1-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.更多还原