Bifurcation analysis of an Internet congestion control model

We investigate the bifurcation behavior of a discrete-time model of Internet congestion control system, which stands for a single link shared by multiple sources. By choosing the gain parameter and the number of sources as bifurcation parameters, we prove the existence of period doubling bifurcation in the model and study the stability of bifurcation. We also find that chaotic behavior of the model can be controlled by limiting the amplitudes of the sending rates.

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

[2]  P. Akishin,et al.  Internet Traffic Dynamics: Local Area Network Study , 2003 .

[3]  QUTdN QeO,et al.  Random early detection gateways for congestion avoidance , 1993, TNET.

[4]  Steven H. Low,et al.  REM: active queue management , 2001, IEEE Netw..

[5]  Xiao Fan Wang,et al.  A stability theorem for Internet congestion control , 2002, Syst. Control. Lett..

[6]  Rayadurgam Srikant,et al.  Analysis and design of an adaptive virtual queue (AVQ) algorithm for active queue management , 2001, SIGCOMM.

[7]  Yin Zhang,et al.  Understanding the performance of many TCP flows , 2001, Comput. Networks.

[8]  R. Srikant,et al.  An adaptive virtual queue (AVQ) algorithm for active queue management , 2004, IEEE/ACM Transactions on Networking.

[9]  Laurent Massoulié,et al.  Stability of distributed congestion control with heterogeneous feedback delays , 2002, IEEE Trans. Autom. Control..

[10]  L. P. D. G. Mircea.  Internet Traffic Dynamics : Local Area Network Study , 2004 .

[11]  Frank Kelly,et al.  Models for a self–managed Internet , 2000, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[12]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[13]  Guanrong Chen,et al.  Hopf bifurcation in an Internet congestion control model , 2004 .

[14]  R. Srikant,et al.  Global stability of congestion controllers for the internet , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[15]  Glenn Vinnicombe,et al.  On the stability of end-to-end congestion control for the internet , 2001 .

[16]  Ramesh Johari,et al.  End-to-end congestion control for the internet: delays and stability , 2001, TNET.