Stochastic Modeling and Convergence Analysis of Internet Routers

ZHOU Jun; ZHANG Jian; YANG Shunfeng

doi:10.21656/1000-0887.420026

Volume 43 Issue 2

Feb. 2022

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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

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

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Stochastic Modeling and Convergence Analysis of Internet Routers

doi: 10.21656/1000-0887.420026

ZHOU Jun^{1, 2
,},
ZHANG Jian¹,
YANG Shunfeng^{1
,
,}

1.
School of Mathematics and Physics, Southwest Forestry University, Kunming 650224, P.R.China
2.
College of Information Science and Technology, Donghua University, Shanghai 201620, P.R.China

Received Date: 2021-01-27
Accepted Date: 2021-01-27
Rev Recd Date: 2021-05-26

Available Online: 2022-01-10

Publish Date: 2022-02-01

Abstract

Abstract

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.
- route convergence,
- white Gaussian noise,
- Laplacian matrix,
- Markov switching,
- Itô formula

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References(15)

References

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