Internet路由器随机建模与收敛性分析  

Stochastic Modeling and Convergence Analysis of Internet Routers

作　　者：周军 张健[1] 杨顺枫 ZHOU Jun;ZHANG Jian;YANG Shunfeng(School of Mathematics and Physics,Southwest Forestry University,Kunming 650224,P.R.China;College of Information Science and Technology,Donghua University,Shanghai 201620,P.R.China)

机构地区：[1]西南林业大学数理学院,昆明650224 [2]东华大学信息科学与技术学院,上海201620

出　　处：《应用数学和力学》2022年第2期207-214,共8页Applied Mathematics and Mechanics

基　　金：云南省基础研究计划(202001AT070112)。

摘　　要：目前建立的路由收敛模型大部分都是确定性模型,而路由器在收敛过程中存在丢包、链路噪声、互连拓扑结构突变等现象.针对这些随机问题,该文引入Bernoulli白序列分布、Wiener过程、Markov过程,提出了一种新的随机动力系统模型,应用随机微分方程理论和随机分析方法得出其路由收敛的充分条件,结果证明,随机环境下路由状态收敛与路由器连接拓扑的Laplace矩阵、Markov切换的平稳分布、网络中数据包的成功传输率以及噪声强度息息相关.最后通过一个数值实例验证了相关结论的有效性.The existent route convergence models are mainly deterministic ones, and various phenomena, such as packet losses, link noises, and sudden changes in interconnecting topology will occur in the route convergence process. Aimed at these random problems, a new stochastic dynamic system model was proposed by means of the Bernoulli white sequence distribution, the Wiener process and the Markov process. Based on the stochastic differential equation theory and the stochastic analysis methods, the sufficient conditions for the route convergence were given. The results prove that, the convergence of the routing state in a random environment is closely related to the Laplacian matrix of the router connection topology, the smooth distribution of the Markov switching, the successful transmission rate of the data packets, and the noise intensity in the network. Finally, a numerical example illustrates the effectiveness of the results.

关 键 词：路由收敛 Gauss白噪声 LAPLACE矩阵 Markov切换 It?公式 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]