September  2011, 16(2): 653-668. doi: 10.3934/dcdsb.2011.16.653

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

1. 

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

Received  February 2010 Revised  November 2010 Published  June 2011

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.
Citation: Shu Zhang, Jian Xu. Time-varying delayed feedback control for an internet congestion control model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 653-668. doi: 10.3934/dcdsb.2011.16.653
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show all references

References:
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in "Proceedings of the 42nd IEEE Conference on Decision and Control," (2003), 1092-1097. Google Scholar

[2]

Discrete Contin. Dyn. Syst. Ser A, 25 (2009), 751-775. doi: 10.3934/dcds.2009.25.751.  Google Scholar

[3]

International Journal of Bifurcation and Chaos, 15 (2005), 2643-2651. doi: 10.1142/S0218127405013587.  Google Scholar

[4]

Journal of Dynamics and Differential Equations, 17 (2005), 353-389. doi: 10.1007/s10884-005-3145-y.  Google Scholar

[5]

Nonlinear Dynamics, 30 (2002), 323-335. doi: 10.1023/A:1021220117746.  Google Scholar

[6]

Nonlinear Analysis: Real World Applications, 10 (2009), 2873-2883. doi: 10.1016/j.nonrwa.2008.09.007.  Google Scholar

[7]

IEEE/ACM Transctions on Networks, 1 (1993), 397-413. Google Scholar

[8]

Nonlinear Dynamics, 30 (2002), 103-154. doi: 10.1023/A:1020455821894.  Google Scholar

[9]

Chaos, 18 (2008), 043104-1-13. doi: 10.1063/1.2998220.  Google Scholar

[10]

Nonlinear Analysis: Real World Applications, 9 (2008), 1292-1309. doi: 10.1016/j.nonrwa.2007.03.006.  Google Scholar

[11]

Nonlinear Analysis: Real World Applications, 9 (2008), 1768-1793. doi: 10.1016/j.nonrwa.2007.05.014.  Google Scholar

[12]

World Publishing Corporation, Beijing, China, 2003. Google Scholar

[13]

ACM SIGCOMM Computer Communication Review, 18 (1988), 314-329. doi: 10.1145/52325.52356.  Google Scholar

[14]

in "Proceedings of ICARCV," (2004), 590-594. Google Scholar

[15]

Philos Trans Roy Soc A, 358 (2000), 2335-2348. doi: 10.1098/rsta.2000.0651.  Google Scholar

[16]

J. Oper. Res. Soc., 49 (1998), 237-252. Google Scholar

[17]

IEEE/ACM Transactions on Networking, 7 (2003), 689-702. doi: 10.1109/TNET.2003.818183.  Google Scholar

[18]

edition, Springer, 1997. Google Scholar

[19]

Chaos Solitons & Fractals, 19 (2004), 853-862. doi: 10.1016/S0960-0779(03)00269-8.  Google Scholar

[20]

in "Proceedings of the 42nd IEEE Conference on Decision and Control," (2003), 3048-3057. Google Scholar

[21]

Nonlinear Analysis: Real World Applications, 11 (2010), 1491-1501. doi: 10.1016/j.nonrwa.2009.03.005.  Google Scholar

[22]

Systems & Control Letters, 46 (2002), 165-172. doi: 10.1016/S0167-6911(02)00123-8.  Google Scholar

[23]

IEEE Transactions on Automatic Control, 50 (2005), 1135-1146. doi: 10.1109/TAC.2005.852566.  Google Scholar

[24]

Performance Evaluation, 64 (2007), 266-275. doi: 10.1016/j.peva.2006.05.005.  Google Scholar

[25]

Electrical Engineering in Japan, 146 (2004), 43-53. doi: 10.1002/eej.10217.  Google Scholar

[26]

Birkhäuser, Boston, 2004.  Google Scholar

[27]

Systems & Control Letters, 45 (2002), 81-85. doi: 10.1016/S0167-6911(01)00165-7.  Google Scholar

[28]

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[29]

J. Math. Anal. Appl., 332 (2007), 1010-1027. doi: 10.1016/j.jmaa.2006.10.062.  Google Scholar

[30]

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[31]

SIAM J. Applied Dynamical Sysyems, 6 (2007), 29-60. doi: 10.1137/040614207.  Google Scholar

[32]

Chaos, Solitons & Fractals, 25 (2005), 1093-1105. doi: 10.1016/j.chaos.2004.11.085.  Google Scholar

[33]

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