Abstract
A class of window-based network congestion control system with communication delays is studied. By analyzing the network system with communication delay, a critical value of the window size to ensure the stability of network is obtained, and a critical value of the delay to ensure the system stability is presented. Enlarging the delay across the critical value, we find that the congestion control system exhibits Hopf bifurcation.
This work is supported by the National Postdoctoral Science Foundation of China (under the grant 20060390972), and the Science Foundation of Office of Education of Shandong Province (under the grant J06G03) of China.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Jacobson, V.: Congestion Avoidance and Control. In: Proceedings of ACM SIGCOMM’88, Stanford, CA, pp. 314–329 (1988)
Mahdavi, J., Floyd, S.: TCP-friendly Unicast Rate-based Flow Control (January 1997), http://www.psc.edu/networking/tcp_friendly.html
Floyd, S., Handley, M., Padhye, J.: Equation-based Congestion Control for Unicast Applications. In: Proc. SIGCOMM Symposium on Communications Architecture and Protocol, August 2000, pp. 43–56 (2000)
Bansal, D., Balakrishnan, H.: Binomial Congestion Algorithms. In: IEEE INFOCOM 2001, Anchorage, AK, April 2001, pp. 631–640 (2001)
Yang, Y., Lam, S.: General AIMD Congestion Control. Technical Report TR-2000-09, University of Texas at Austin (May 2000), http://www.cs.utexas.edu/users/lam/NRL/
Brakmo, L., Peterson, L.: TCP Vegas: End to End Congestion Avoidance on a Global Internet. IEEE J. Select. Areas in communications 13, 1465–1480 (1995)
Kelly, F.P., Maulloo, A., Tan, D.: Rate Control for Communication Networks: Shadow Prices, Proportional Fairness, and Stability. J. Oper. Res. Soc. 49, 237–252 (1998)
Johari, R., Tan, D.: End-to-end Congestion Control for the Internet: Delays and Stability. IEEE/ACM Trans. Networking 9, 818–832 (2001)
Massoulie, L.: Stability of Distributed Congestion Control with Heterogeneous Feedback Delays. IEEE Trans. Automatic Control 47, 895–902 (2002)
Tian, Y., Yang, H.: Stability of the Internet Congestion Control with Diverse Delays. Automatica 40, 1533–1541 (2004)
Cooke, K., Grossman, Z.: Discrete Delay, Distributed Delay and Stability Switches. J. Math. Anal. Appl. 86, 592–627 (1982)
Vinnicombe, G.: On the Stability of Networks Operating TCP-like Congestion Control. In: Proceedings of IFAC World congress (2002)
Kelly, F.: Fairness and Stability of End-to-end Congestion Control. European Journal of Control 9, 159–176 (2003)
Hale, J.: Theory of functional differential equations. Springer, Berlin (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yang, Hy., Wang, Fs., Zhu, Xl., Zhang, Sy. (2007). Dynamics of Window-Based Network Congestion Control System. In: Liu, D., Fei, S., Hou, ZG., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72383-7_30
Download citation
DOI: https://doi.org/10.1007/978-3-540-72383-7_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72382-0
Online ISBN: 978-3-540-72383-7
eBook Packages: Computer ScienceComputer Science (R0)