Controlling bifurcations and chaos in TCP–UDP–RED

Abstract We study the bifurcation and chaotic behavior of the Transmission Control Protocol (TCP) and User Datagram Protocol (UDP) network with Random Early Detection (RED) queue management. These bifurcation and chaotic behaviors may cause heavy oscillation of an average queue length and induce network instability. We propose an impulsive control method for controlling bifurcations and chaos in the internet congestion control system. The theoretical analysis and the simulation experiments show that this method can obtain the stable average queue length without sacrificing the other advantages of RED.

[1]  Feng Liu,et al.  Impulsive control of bifurcations , 2009, Math. Comput. Simul..

[2]  V. Jacobson,et al.  Congestion avoidance and control , 1988, CCRV.

[3]  Eyad H. Abed,et al.  Stabilization of period doubling bifurcations and implications for control of chaos , 1994 .

[4]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[5]  João Pedro Hespanha,et al.  Hybrid Modeling of TCP Congestion Control , 2001, HSCC.

[6]  Victor Firoiu,et al.  A study of active queue management for congestion control , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[7]  Eyad H. Abed,et al.  Nonlinear instabilities in TCP-RED , 2002, IEEE/ACM Transactions on Networking.

[8]  Lima,et al.  Suppression of chaos by resonant parametric perturbations. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[9]  Guanrong Chen,et al.  Bifurcation Control: Theories, Methods, and Applications , 2000, Int. J. Bifurc. Chaos.

[10]  Tao Yang,et al.  In: Impulsive control theory , 2001 .

[11]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[12]  Andras Veres,et al.  The chaotic nature of TCP congestion control , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[13]  Guanrong Chen,et al.  On feedback control of chaotic continuous-time systems , 1993 .

[14]  Hua O. Wang,et al.  Bifurcation control of a chaotic system , 1995, Autom..

[15]  Gauthier,et al.  Stabilizing unstable periodic orbits in fast dynamical systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  Matthew Mathis,et al.  The macroscopic behavior of the TCP congestion avoidance algorithm , 1997, CCRV.

[17]  Guanrong Chen,et al.  Hybrid control of period-doubling bifurcation and chaos in discrete nonlinear dynamical systems , 2003 .

[18]  Zhen Chen,et al.  Hopf bifurcation Control for an Internet Congestion Model , 2005, Int. J. Bifurc. Chaos.

[19]  Van Jacobson,et al.  Random early detection gateways for congestion avoidance , 1993, TNET.