带工作故障的M/M/1重试排队流模型系统性能分析
The Performance Analysis of a Retrial M/M/1 Flow Queue Model with Working Breakdowns
DOI: 10.12677/AAM.2022.112082, PDF,    国家自然科学基金支持
作者: 孙红霜, 叶晴晴：南京信息工程大学数学与统计学院，江苏 南京
关键词: 流模型；工作故障；重试排队；矩阵几何解；Fluid Queue Model； Working Breakdown； Retrial Queue； Matrix Geometrical Solution
摘要: 为了拓展流排队模型的相关理论，本文研究了带有故障和重试系统的M/M/1排队驱动系统的流模型。基于矩阵几何解法对模型的主要性能指标进行了研究，对构建的微分方程进行推导，得到了系统的稳态库存量的LST及其均值。最后通过数值例子说明不同参数对各项性能指标的影响，为现实情况中的故障和重试排队服务系统提供参考。
Abstract: In order to expand the related theory of stream queuing model, this paper studies streaming of M/M/1 queuing drive system with faults and retry systems. Based on the matrix geometry method, the main performance indicator of the model is studied, and the construction of the differential equation is derived, and the system’s steady-state stock LST and its mean are obtained. Finally, numerical examples illustrate the influence of different parameters to various performance indicators, provide reference for the fault and retry queuing service systems in realities.
文章引用：孙红霜, 叶晴晴. 带工作故障的M/M/1重试排队流模型系统性能分析[J]. 应用数学进展, 2022, 11(2): 769-780. https://doi.org/10.12677/AAM.2022.112082

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