具有工作故障的流模型近似解分析
Asymptotic Solution of the Fluid Model with Working Breakdown Policy
DOI: 10.12677/AAM.2023.122079, PDF,    国家自然科学基金支持
作者: 刘煜飞, 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；归一化技术；Fluid Model； Working Breakdown； Uniformization Technique
摘要: 本文分析了具有工作故障策略的流模型。当流模型处于正常工作状态时，服务台以较高速率为顾客提供服务，若发生故障，服务台将进入工作故障状态，同时维修立刻开始，期间服务台服务速率降低。当维修完成时，流模型将进入正常工作状态。通过归一化技术(Uniformization Technique)与递推公式，得到了流模型库存量尾分布函数的近似表达式，并得到了稳态下库存量各阶矩的表达式。最后通过数值例子分析了系统性能指标随参数的变化趋势。
Abstract: In this paper, we analyze the fluid model with working breakdown policy. During the normal work-ing period, the service serves customers at a high rate. When breakdown happens, server will turn into the partial working period and continue to provide service to arriving customers, but with a lower rate. When the repair is completed, the fluid model will enter the normal working period. Through the recursive formula and Uniformization Technique, we obtain the recursive expression of the tail joint distribution function and the expressions of each moment of the buffer content in stability condition are obtained. Finally, the variation trend of system performance index with pa-rameters is analyzed by numerical examples.
文章引用：刘煜飞, 叶晴晴. 具有工作故障的流模型近似解分析[J]. 应用数学进展, 2023, 12(2): 771-780. https://doi.org/10.12677/AAM.2023.122079

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