带有反馈的M/M/1重试工作休假排队模型
An M/M/1 Retrial Queue with Working Vacation and Feedback
DOI: 10.12677/AAM.2019.82024, PDF,   
作者: 李俊潼, 李 涛, 徐金萍：山东理工大学数学与统计学院，山东 淄博
关键词: 重试；工作休假；反馈；随机条件分解；Retrial； Working Vacation； Collision； Conditional Stochastic Decomposition
摘要: 研究带有反馈、重试和工作休假的M/M/1排队模型：当系统为空时，服务员进入工作休假，以低速率提供服务，若顾客到达时服务员忙，则顾客进入重试组等待，接收服务完毕的顾客以概率p离开系统或以概率p(p=1-p)返回系统重新排队。对该模型，运用拟生灭过程和矩阵几何解的方法，得到平稳队长及一些相应指标，并给出队长分解，最后，利用数值例子进行解释。
Abstract: In this paper, we considered an M/M/1 retrial queue with working vacation and feedback. In order to obtain the necessary and sufficient condition for system to be stable, the matrix-analytic method is used. The stationary probability distribution and some performance measures were also derived. Then we give the conditional stochastic decomposition for the queue length in the orbit when the server is busy. Finally, the model parameters on the system's characteristics are presented by some numerical examples.
文章引用：李俊潼, 李涛, 徐金萍. 带有反馈的M/M/1重试工作休假排队模型[J]. 应用数学进展, 2019, 8(2): 210-218. https://doi.org/10.12677/AAM.2019.82024

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