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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

  • [1] GRIFFIN T G, SHEPHERD F B, WILFONG G. The stable paths problem and interdomain routing[J]. IEEE/ACM Transactions on Networking, 2002, 10(2): 232-243. doi: 10.1109/90.993304
    [2] 张微, 吴建平, 徐恪, 等. 边界网关协议BGP4路由收敛问题研究进展[J]. 小型微型计算机系统, 2006, 27(5): 818-824. (ZHANG Wei, WU Jianping, XU Ke, et al. Research progress of convergence problem of border gateway protocol 4 (BGP4)[J]. Mini-Micro Systems, 2006, 27(5): 818-824.(in Chinese) doi: 10.3969/j.issn.1000-1220.2006.05.012
    [3] LABOVITZ C, AHUJA A, WATTENHOFER R, et al. The impact of Internet policy and topology on delayed routing convergence[C]//Proceedings IEEE INFOCOM 2001 Conference on Computer Communications. 2001.
    [4] 赵金晶, 朱培栋, 周丽涛. 域间路由协议BGP收敛时间的定量分析及预测[J]. 计算机工程与科学, 2007, 29(9): 56-57. (ZHAO Jinjing, ZHU Peidong, ZHOU Litao. Analysis and prediction on the BGP convergence time[J]. Computer Engineering and Science, 2007, 29(9): 56-57.(in Chinese) doi: 10.3969/j.issn.1007-130X.2007.09.016
    [5] 张昕, 赵海, 李超. 一种基于多项复杂特征的Internet 路由级拓扑建模方法[J]. 电子学报, 2008, 36(1): 57-63. (ZHANG Xin, ZHAO Hai, LI Chao. A model for router-level topology of Internet based on complex characters[J]. Acta Electronica Sinica, 2008, 36(1): 57-63.(in Chinese) doi: 10.3321/j.issn:0372-2112.2008.01.010
    [6] 李鹤帅, 朱俊虎, 王清贤, 等. Internet建模的关键: 研究AS间路由器级连接[J]. 计算机科学, 2016, 43(9): 135-139. (LI Heshuai, ZHU Junhu, WANG Qingxian, et al. Key of Internet modeling-looking inside inter-AS router-level connection[J]. Computer Science, 2016, 43(9): 135-139.(in Chinese) doi: 10.11896/j.issn.1002-137X.2016.09.026
    [7] PIETRABISSA A, CELSI L R. Discrete-time selfish routing converging to the wardrop equilibrium[J]. IEEE Transactions on Automatic Control, 2019, 64(3): 1288-1294. doi: 10.1109/TAC.2018.2847602
    [8] SUN G, BIN S. Router-level Internet topology evolution model based on multi-subnet composited complex network model[J]. Journal of Internet Technology, 2017, 18(6): 1-8.
    [9] ABDULKADHIM M. Routing protocols convergence activity and protocols related traffic simulation with it’s impact on the network[J]. International Journal of Computer Science Engineering and Technology, 2015, 5(3): 40-43.
    [10] RABBANI H, BEYGI L, GHOSHOONI S, et al. Quality of transmission aware optical networking using enhanced Gaussian noise model[J]. Journal of Lightwave Technology, 2019, 37(3): 831-838. doi: 10.1109/JLT.2018.2881607
    [11] 赵玮, 任凤丽. 基于牵制控制的多智能体系统的有限时间与固定时间一致性[J]. 应用数学和力学, 2021, 42(3): 299-307. (ZHAO Wei, REN Fengli. Finite-time and fixed-time consensus for multi-agent systems via pinning control[J]. Applied Mathematics and Mechanics, 2021, 42(3): 299-307.(in Chinese)
    [12] ZHOU J, CAI T T, ZHOU W N, et al. Master-slave synchronization for coupled neural networks with Markovian switching topologies and stochastic perturbation[J]. International Journal of Robust and Nonlinear Control, 2018, 28(6): 2249-2263. doi: 10.1002/rnc.4013
    [13] NI W, CHEN D. Leader-following consensus of multi-agent systems under fixed and switching topologies[J]. System and Control Letters, 2010, 59(3/4): 209-217.
    [14] MAO X R, YUAN C G. Stochastic Differential Equations With Markovian Switching[M]. London: Imperial College Press, 2006.
    [15] 马丽, 马瑞楠. 一类随机泛函微分方程带随机步长的EM逼近的渐近稳定[J]. 应用数学和力学, 2019, 40(1): 97-107. (MA Li, MA Ruinan. Almost sure asymptotic stability of the Euler-Maruyama method with random variable stepsizes for stochastic functional differential equations[J]. Applied Mathematics and Mechanics, 2019, 40(1): 97-107.(in Chinese) doi: 10.1007/s10483-019-2403-6
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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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