Time-varying delayed feedback control for an internet congestion control model

Shu Zhang; Jian Xu

doi:10.3934/dcdsb.2011.16.653

Article Contents

2011, Volume 16, Issue 2: 653-668. Doi: 10.3934/dcdsb.2011.16.653

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Time-varying delayed feedback control for an internet congestion control model

Shu Zhang^1, and
Jian Xu^1,

1.
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092

Received: January 31, 2010

Revised: October 31, 2010

Published: August 2011

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Abstract

A proportionally-fair controller with time delay is considered to control Internet congestion. The time delay is chosen to be a controllable parameter. To represent the relation between the delay and congestion analytically, the method of multiple scales is employed to obtain the periodic solution arising from the Hopf bifurcation in the congestion control model. A new control method is proposed by perturbing the delay periodically. The strength of the perturbation is predicted analytically in order that the oscillation may disappear gradually. It implies that the proved control scheme may decrease the possibility of the congestion derived from the oscillation. The proposed control scheme is verified by the numerical simulation.

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Mathematics Subject Classification: Primary: 34K07, 34K13, 34K18; Secondary: 94C99.

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