Stability and convergence of TCP-like congestion controllers in a many-flows regime

With the rapid growth of Internet, parameter design and analysis for large-scale networks has become a topic of active interest. Since simulation of such large scale systems is not easy, deterministic fluid models have been widely used for both qualitative understanding of the behavior, as well as parameter design for such networks. In this paper, we first study a deterministic fluid model for Internet congestion control when there are multiple TCP-like flows present. We provide conditions under which such a system is globally asymptotically stable in the presence of feedback delay. We then study the corresponding system with the addition of web mice and other nonresponsive flows modeled as stochastic disturbances. We show that, when there are a large number of flows, choosing parameters based on the global stability criterion for the deterministic system (with the noise replaced by its mean value) ensures global stability for the stochastic system as well. Numerical examples and simulation results with some popular active queue management mechanisms validate the parameter choices from analysis. The results indicate that a system with multiple TCP-like flows is globally stable as long as the bandwidth-delay product per flow is not very small.

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

[2]  R. Srikant,et al.  End-to-end congestion control schemes: utility functions, random losses and ECN marks , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

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

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

[5]  R. Srikant,et al.  Mean FDE models for Internet congestion control under a many-flows regime , 2004, IEEE Transactions on Information Theory.

[6]  J. Kato.  Stability in functional differential equations , 1980 .

[7]  Sally Floyd,et al.  TCP and explicit congestion notification , 1994, CCRV.

[8]  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.

[9]  Donald F. Towsley,et al.  On designing improved controllers for AQM routers supporting TCP flows , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[10]  Sean P. Meyn,et al.  Bounds on the throughput of congestion controllers in the presence of feedback delay , 2003, TNET.

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

[12]  François Baccelli,et al.  Interaction of TCP flows as billiards , 2005, IEEE/ACM Transactions on Networking.

[13]  R. Srikant,et al.  Global stability of congestion controllers for the Internet , 2003, IEEE Trans. Autom. Control..

[14]  Fernando Paganini,et al.  Scalable laws for stable network congestion control , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

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

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

[17]  D. Lapsley,et al.  Random early marking for Internet congestion control , 1999, Seamless Interconnection for Universal Services. Global Telecommunications Conference. GLOBECOM'99. (Cat. No.99CH37042).