Applied Mathematics and Mechanics

, Volume 40, Issue 1, pp 25–48 | Cite as

Suppression of oscillatory congestion via trunk link bandwidth and control gain in star network

  • Sainan Wang
  • Shu Zhang
  • Jian XuEmail author
Open Access


The time delay-induced instability in an Internet congestion control model is investigated. The star topology is considered, and the link bandwidth ratio and the control gain are selected as the tunable parameters for congestion suppression. The stability switch boundary is obtained by the eigenvalue analysis for the linearized system around the equilibrium. To investigate the oscillatory congestion when the equilibrium becomes unstable, the center manifold reduction and the normal form theory are used to study the periodic oscillation induced by the delay. The theoretical analysis and numerical simulation show that the ratio between bandwidths of the trunk link and the regular link, rather than these bandwidths themselves, is crucial for the stability of the congestion control system. The present results demonstrate that it is not always effective to increase the link bandwidth ratio for stabilizing the system, and for some certain delays, adjusting the control gain is more efficient.

Key words

Internet congestion control Hopf bifurcation delayed differential equation stability normal form 

Chinese Library Classification

O193 O137+.1 

2010 Mathematics Subject Classification



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© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provided a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.School of Aerospace Engineering and Applied MechanicsTongji UniversityShanghaiChina

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