带有伯努利反馈的Geo/Geo/1队列中性能度量的经典和贝叶斯估计
Classical and Bayesian Estimations of Performance Measures in Geo/Geo/1 Queue with Bernoulli Feedback
DOI: 10.12677/AAM.2023.1211453, PDF,   
作者: 刘欣颖：南京航空航天大学数学学院，江苏 南京
关键词: 贝叶斯推理；伯努利反馈；Geo/Geo/1队列；UMVUE；Bayesian Inference； Bernoulli Feedback； Geo/Geo/1 Queue； UMVUEs
摘要: 在本文中，我们从统计角度研究带有伯努利反馈的Geo/Geo/1队列。考虑了经典和贝叶斯框架下的参数和系统性能的估计。我们尝试研究各种排队特征的一致最小方差无偏估计量(UMVUE)和封闭的贝叶斯估计量。此外，我们进行了蒙特卡洛模拟，结果表明所构建的估计器具有大样本收敛特性，可用于近似有限样本中的性能度量，估计器选择没有绝对最优，但封闭形式的贝叶斯估计器在统计实践中更受欢迎，结果为我们在不同系统性能估计场景下最优估计器的选择提供了指导。
Abstract: In this paper, we consider a Geo/Geo/1 queue with Bernoulli feedback from the statistical perspec-tive. The estimations of parameters and system performances under classical and Bayesian frame-works are considered. We attempt to study the uniform minimum-variance unbiased estimators (UMVUEs) and the closed Bayesian estimators for various queueing characteristics. In addition, we conduct Monte Carlo simulations and the results show that the estimators have large sample con-vergence characteristics and can be used to approximate performance measures in finite samples. The estimator selection is not absolute optimal, but the closed form Bayesian estimator is more popular in statistical practice. The results provide guidance for us to choose the optimal estimator in different application scenarios.
文章引用：刘欣颖. 带有伯努利反馈的Geo/Geo/1队列中性能度量的经典和贝叶斯估计[J]. 应用数学进展, 2023, 12(11): 4622-4631. https://doi.org/10.12677/AAM.2023.1211453

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