Abstract
Flow control and congestion control are becoming increasingly important nowadays due to explosive expansion and rapid growth of traffic in the Internet. They are inherently very complex nonlinear dynamic problems. Improper configuration of parameters can easily lead to the instability of network flow control system. An appropriate Lyapunov function is introduced aiming at the time-dependent model of deterministic continuous flow control system. Global asymptotically stability of flow control system was investigated in-depth without time delay and with bounded time varying delays, which solves the difficulty of parameter configuration of flow controller in the network routers very well. This stability result not only is consistent with former research neglecting time delay, but also provides novel criterions in order to avoid instability of network under a more general topology.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Low, S.H.: Network Flow Control. Technical Report (2002), Available at http://netlab.caltech.edu
Kelly, F.P., et al.: Mathematical Modeling of the Internet. In: Fourth International Congress on Industrial and Applied Mathematics, Edinburgh, Scotland (July 1999)
Kelly, F.P., Maulloo, A., Tan, D.: Rate Control for Communication Networks: shadow prices, proportional fairness and Stability. Journal of Operation Research, Soc. 49(3), 237–252 (1998)
Low, S.H., Lapsley, D.E.: Optimization Flow Control- I: Basic Algorithm and Convergence. IEEE/ACM Trans. on Networking 7(6), 861–874 (1999)
Athuraliya, S., Low, S.H., Li, V.H., Yin, Q.: REM: Active Queue Management. IEEE Networks 15(3), 48–53 (2001)
Paganini, F.: A Global Stability Result in Network Flow Control. Systems & Control Letters 46, 165–172 (2002)
Johari, R., Tan, D.K.H.: End-to-End Congestion Control for the Internet: Delays and Stability. IEEE/ACM Transactions on Networking 9(6) (December 2001)
Deb, S., Shakkottai, S., Srikant, R.: Stability and Convergence of TCP-Like Congestion Controllers in a Many-Flow Regime. In: Proceedings of IEEE INFOCOM (2003)
Wang, X.F., Chen, G.R., Kob, K.T.: A Stability Theorem for Internet Congestion Control. Systems & Control Letters 45, 81–85 (2002)
Sun, Y.J., Hsieh, J.G., Yang, H.C.: On the Stability of Uncertain Systems with Multiple Time-Varying Delays. IEEE Trans. on Automatic Control 42(1) (1997)
Athuraliya, S., Low, S.H.: Optimization Flow Control–II: Implementation, Available at http://netlab.caltech.edu/
Xu, B., Liu, Y.: An Improved Razumikhin-Type Theorem and Its Applications. IEEE Trans. on Automatic Control 39, 839–841 (1994)
Long, C.N., Wu, J., Guan, X.P.: Local stability of REM algorithm with time-varying delays. IEEE Communications Letters 7(3), 142–144 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xu, Y., Wang, L., Guan, Z., Wang, H.O. (2004). Global Stability of Optimization Based Flow Control with Time-Varying Delays. In: Liew, KM., Shen, H., See, S., Cai, W., Fan, P., Horiguchi, S. (eds) Parallel and Distributed Computing: Applications and Technologies. PDCAT 2004. Lecture Notes in Computer Science, vol 3320. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30501-9_69
Download citation
DOI: https://doi.org/10.1007/978-3-540-30501-9_69
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24013-6
Online ISBN: 978-3-540-30501-9
eBook Packages: Computer ScienceComputer Science (R0)