中国物理B ›› 2008, Vol. 17 ›› Issue (1): 105-110.doi: 10.1088/1674-1056/17/1/019

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Hybrid control of bifurcation and chaos in stroboscopic model of Internet congestion control system

朱杰1, 丁大为2, 罗晓曙3   

  1. (1)Department of Electronic Engineering, Shanghai Jiaotong University, Shanghai 200240, China; (2)Department of Electronic Engineering, Shanghai Jiaotong University, Shanghai 200240, China \; School of Electronic Science and Technology, Anhui University, Hefei 230039, China; (3)Department of Physics and Electronic Science, Guangxi Normal University, Guilin 541004, China
  • 出版日期:2008-01-20 发布日期:2008-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 70571017).

Hybrid control of bifurcation and chaos in stroboscopic model of Internet congestion control system

Ding Da-Wei (丁大为)a)b)†, Zhu Jie(朱杰)a), and Luo Xiao-Shu(罗晓曙)c)   

  1. a Department of Electronic Engineering, Shanghai Jiaotong University, Shanghai 200240, China; b School of Electronic Science and Technology, Anhui University, Hefei 230039, China; c Department of Physics and Electronic Science, Guangxi Normal University, Guilin 541004, China
  • Online:2008-01-20 Published:2008-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 70571017).

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摘要： Interaction between transmission control protocol (TCP) and random early detection (RED) gateway in the Internet congestion control system has been modelled as a discrete-time dynamic system which exhibits complex bifurcating and chaotic behaviours. In this paper, a hybrid control strategy using both state feedback and parameter perturbation is employed to control the bifurcation and stabilize the chaotic orbits embedded in this discrete-time dynamic system of TCP/RED. Theoretical analysis and numerical simulations show that the bifurcation is delayed and the chaotic orbits are stabilized to a fixed point, which reliably achieves a stable average queue size in an extended range of parameters and even completely eliminates the chaotic behaviour in a particular range of parameters. Therefore it is possible to decrease the sensitivity of RED to parameters. By using the hybrid strategy, we may improve the stability and performance of TCP/RED congestion control system significantly.

关键词: chaos control, dynamical systems, congestion control, bifurcation

Abstract: Interaction between transmission control protocol (TCP) and random early detection (RED) gateway in the Internet congestion control system has been modelled as a discrete-time dynamic system which exhibits complex bifurcating and chaotic behaviours. In this paper, a hybrid control strategy using both state feedback and parameter perturbation is employed to control the bifurcation and stabilize the chaotic orbits embedded in this discrete-time dynamic system of TCP/RED. Theoretical analysis and numerical simulations show that the bifurcation is delayed and the chaotic orbits are stabilized to a fixed point, which reliably achieves a stable average queue size in an extended range of parameters and even completely eliminates the chaotic behaviour in a particular range of parameters. Therefore it is possible to decrease the sensitivity of RED to parameters. By using the hybrid strategy, we may improve the stability and performance of TCP/RED congestion control system significantly.

Key words: chaos control, dynamical systems, congestion control, bifurcation

中图分类号:  (Control of chaos, applications of chaos)

  • 05.45.Gg
05.45.Pq (Numerical simulations of chaotic systems) 02.30.Oz (Bifurcation theory)