Necessary and sufficient conditions for Hopf bifurcation in exponential RED algorithm with communication delay

Guo, Songtao; Liao, Xiaofeng; Li, Qun; Li, Chuandong

doi:10.1016/j.nonrwa.2007.05.014

Cited by 26 publications

(13 citation statements)

References 23 publications

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“…The answer to this question is related to the nonlinear dynamics of the congestion control model. Therefore, in recent years, there has been a rapidly growing interest in the nonlinear dynamical behavior of congestion control model, such as bifurcations and chaos [8][9][10][11][12][13][14]. For example, in ref.…”

Section: Introductionmentioning

confidence: 99%

Oscillation control for n-dimensional congestion control model via time-varying delay

Shu

2011

Sci. China Technol. Sci.

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Time delay or round trip time (RTT) is an important parameter in the model of Internet congestion control. On the one hand, the delay may induce oscillation via the Hopf bifurcation. In the present paper, a congestion control model of n dimensions is considered to study the delay-induced oscillation. By linear analysis of the n-dimensional system, the critical delay for the Hopf bifurcation is obtained. To describe the relation between the delay and oscillation analytically, the method of multiple scales (MMS) is employed to obtain the bifurcating periodic solution. On the other hand, it can be understood that the oscillation will increase the risk of congestion for the network system. To avoid the congestion derived from the oscillation, a new control scheme is proposed by perturbing the delay periodically. Particularly, according to our study, it is possible to control the oscillation by perturbing only one of the n delays. This provides a practical scheme for the oscillation control in the real network system. By MMS, the strengths of the perturbations are predicted analytically such that the oscillation disappears. To give an example, an eight-dimensional model is studied in detail. The analytical results are in good agreement with the numerical simulations.internet congestion control, high-dimensional system, Hopf bifurcation, time-varying delay, method of multiple scales Citation:Zhang S, Xu J. Oscillation control for n-dimensional congestion control model via time-varying delay.

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Section: Introductionmentioning

confidence: 99%

Oscillation control for n-dimensional congestion control model via time-varying delay

Shu

2011

Sci. China Technol. Sci.

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“…The results in [12][13][14] have also shown the occurrence of a Hopf bifurcation in a rate control algorithm with a single link and source. In [15][16][17], the explicit conditions and formula determining the direction and stability of the bifurcation are derived to ensure the onset of stable limit cycles as these algorithms with a single link and a single discrete delay just lose local stability. To the best of our knowledge, there are few papers which discuss the double Hopf bifurcation of the congestion control models with multiple delays.…”

Section: Introductionmentioning

confidence: 99%

Hopf and resonant double Hopf bifurcation in congestion control algorithm with heterogeneous delays

2010

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The congestion control algorithm, which has dynamic adaptations at both user ends and link ends, with heterogeneous delays is considered and analyzed. Some general stability criteria involving the delays and the system parameters are derived by generalized Nyquist criteria. Furthermore, by choosing one of the delays as the bifurcation parameter, and when the delay exceeds a critical value, a limit cycle emerges via a Hopf bifurcation. Resonant double Hopf bifurcation is also found to occur in this model. An efficient perturbation-incremental method is presented to study the delay-induced resonant double Hopf bifurcation. For the bifurcation parameter close to a double Hopf point, the approximate expressions of the periodic solutions are updated iteratively by use of the perturbation-incremental method. Simulation results have verified and demonstrated the correctness of the theoretical results.

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“…There have been many papers studying the nonlinear behavior of Internet congestion control mechanisms such as bifurcations and chaos in models of TCP/AQM systems [2,[4][5][6][9][10][12][13][14][15][16]. Ranjan, et al [13] have used a simple discrete model to investigate the nonlinear behavior of a singlesource single-link network.…”

Section: Introductionmentioning

confidence: 99%

“…In recent work [4], the Hopf bifurcation has been studied for a single-link single-source TCP/E-RED algorithm. Also, a similar work for a single link and two sources network model has been studied in [5].…”

Section: Introductionmentioning

confidence: 99%

The condition of Hopf bifurcation occurrence for congestion control system in computer networks with communication delay

Motlagh

Rezaie

Analoui

et al. 2008

2008 10th International Conference on Control, Automation, Robotics and Vision

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In this paper, we study a rate-based congestion control system with communication delay. We drive the condition on delay parameter under which Hopf bifurcation occurs. By taking delay as a bifurcation parameter and changing it, we find the critical value of delay such that the system passes the critical point and a periodic solution bifurcates from the equilibrium point. The model considered in this paper is a nonlinear delay differential equation which stands for a network with fixed communication delay. The simulation of a numerical example is given for justifying the theorical results.

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Necessary and sufficient conditions for Hopf bifurcation in exponential RED algorithm with communication delay

Cited by 26 publications

References 23 publications

Oscillation control for n-dimensional congestion control model via time-varying delay

Oscillation control for n-dimensional congestion control model via time-varying delay

Hopf and resonant double Hopf bifurcation in congestion control algorithm with heterogeneous delays

The condition of Hopf bifurcation occurrence for congestion control system in computer networks with communication delay

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