{"title":"分析计算机网络的线性随机微分方程的协方差","authors":"Hua Fan (樊 华) , Xiuming Shan (山秀明) , Jian Yuan (袁 坚) , Yong Ren (任 勇)","doi":"10.1016/S1007-0214(11)70038-4","DOIUrl":null,"url":null,"abstract":"<div><p><span>Analyses of dynamic systems with random oscillations need to calculate the system covariance matrix, but this is not easy even in the linear case if the random term is not a </span>Gaussian white noise<span>. A universal method is developed here to handle both Gaussian and compound Poisson white noise. The quadratic variations are analyzed to transform the problem into a Lyapunov matrix differential equation. Explicit formulas are then derived by vectorization. These formulas are applied to a simple model of flows and queuing in a computer network. A stability analysis of the mean value illustrates the effects of oscillations in a real system. The relationships between the oscillations and the parameters are clearly presented to improve designs of real systems.</span></p></div>","PeriodicalId":60306,"journal":{"name":"Tsinghua Science and Technology","volume":null,"pages":null},"PeriodicalIF":5.2000,"publicationDate":"2011-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1007-0214(11)70038-4","citationCount":"4","resultStr":"{\"title\":\"Covariances of Linear Stochastic Differential Equations for Analyzing Computer Networks\",\"authors\":\"Hua Fan (樊 华) , Xiuming Shan (山秀明) , Jian Yuan (袁 坚) , Yong Ren (任 勇)\",\"doi\":\"10.1016/S1007-0214(11)70038-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span>Analyses of dynamic systems with random oscillations need to calculate the system covariance matrix, but this is not easy even in the linear case if the random term is not a </span>Gaussian white noise<span>. A universal method is developed here to handle both Gaussian and compound Poisson white noise. The quadratic variations are analyzed to transform the problem into a Lyapunov matrix differential equation. Explicit formulas are then derived by vectorization. These formulas are applied to a simple model of flows and queuing in a computer network. A stability analysis of the mean value illustrates the effects of oscillations in a real system. The relationships between the oscillations and the parameters are clearly presented to improve designs of real systems.</span></p></div>\",\"PeriodicalId\":60306,\"journal\":{\"name\":\"Tsinghua Science and Technology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":5.2000,\"publicationDate\":\"2011-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S1007-0214(11)70038-4\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tsinghua Science and Technology\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1007021411700384\",\"RegionNum\":1,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, INFORMATION SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tsinghua Science and Technology","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007021411700384","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
Covariances of Linear Stochastic Differential Equations for Analyzing Computer Networks
Analyses of dynamic systems with random oscillations need to calculate the system covariance matrix, but this is not easy even in the linear case if the random term is not a Gaussian white noise. A universal method is developed here to handle both Gaussian and compound Poisson white noise. The quadratic variations are analyzed to transform the problem into a Lyapunov matrix differential equation. Explicit formulas are then derived by vectorization. These formulas are applied to a simple model of flows and queuing in a computer network. A stability analysis of the mean value illustrates the effects of oscillations in a real system. The relationships between the oscillations and the parameters are clearly presented to improve designs of real systems.