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Internet路由器随机建模与收敛性分析

周军 张健 杨顺枫

周军,张健,杨顺枫. Internet路由器随机建模与收敛性分析 [J]. 应用数学和力学,2022,43(2):207-214 doi: 10.21656/1000-0887.420026
引用本文: 周军,张健,杨顺枫. Internet路由器随机建模与收敛性分析 [J]. 应用数学和力学,2022,43(2):207-214 doi: 10.21656/1000-0887.420026
ZHOU Jun, ZHANG Jian, YANG Shunfeng. Stochastic Modeling and Convergence Analysis of Internet Routers[J]. Applied Mathematics and Mechanics, 2022, 43(2): 207-214. doi: 10.21656/1000-0887.420026
Citation: ZHOU Jun, ZHANG Jian, YANG Shunfeng. Stochastic Modeling and Convergence Analysis of Internet Routers[J]. Applied Mathematics and Mechanics, 2022, 43(2): 207-214. doi: 10.21656/1000-0887.420026

Internet路由器随机建模与收敛性分析

doi: 10.21656/1000-0887.420026
基金项目: 云南省基础研究计划(202001AT070112)
详细信息
    作者简介:

    周军(1980—),男,讲师,博士(E-mail:zhouchaos@126.com

    杨顺枫(1982—),男,讲师,博士(通讯作者. E-mail:yangshunfeng@126.com

  • 中图分类号: TP393

Stochastic Modeling and Convergence Analysis of Internet Routers

  • 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。

  • 图  1  路由设备网络连接拓扑图

    Figure  1.  The router connection topology

    图  2  2-状态Markov链

    Figure  2.  The 2-state Markov chain

    图  3  5个路由器路由状态第1个分量

    Figure  3.  The 1st element of the 5-router state

    图  4  5个路由器路由状态第2个分量

    Figure  4.  The 2nd element of the 5-router state

    图  5  5个路由器路由状态第3个分量

    Figure  5.  The 3rd element of the 5-router state

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  • 被引次数: 0
出版历程
  • 收稿日期:  2021-01-27
  • 录用日期:  2021-01-27
  • 修回日期:  2021-05-26
  • 网络出版日期:  2022-01-10
  • 刊出日期:  2022-02-01

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