Global stability with time-delay in network congestion control

This paper concerns the global stability of recently proposed laws for network congestion control. In earlier work (Paganini et al. (2001)) it was shown that such laws were able to maintain local dynamic stability on networks of arbitrary delay, capacity and topology. In this paper we give conditions under which the stability can be shown to be global, focusing on the case of a single bottleneck network. The results include: a general boundedness result; a theorem on global asymptotic stability for the case of a single source, or many homogeneous ones, under quite sharp conditions; and a somewhat weaker asymptotic stability theorem for the heterogeneous source case.

[1]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[2]  A. Rantzer,et al.  System analysis via integral quadratic constraints , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[3]  A. Rantzer,et al.  System analysis via integral quadratic constraints , 1997, IEEE Trans. Autom. Control..

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

[5]  Erik I. Verriest,et al.  Stability and Control of Time-delay Systems , 1998 .

[6]  Steven H. Low,et al.  Optimization flow control—I: basic algorithm and convergence , 1999, TNET.

[7]  Alexandre Megretski,et al.  The Zames-Falb IQC for systems with integrators , 2000, IEEE Trans. Autom. Control..

[8]  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).

[9]  M. Safonov,et al.  Stability analysis of a system with time-delayed states , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[10]  F. Paganini.  On the stability of optimization-based flow control , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[11]  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).

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

[13]  Fernando Paganini,et al.  Internet congestion control , 2002 .

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

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

[16]  Fernando Paganini,et al.  Linear stability of TCP/RED and a scalable control , 2003, Comput. Networks.

[17]  R. Srikant,et al.  End-to-end congestion control schemes: utility functions, random losses and ECN marks , 2003, TNET.

[18]  Fernando Paganini,et al.  A new TCP congestion control with empty queues and scalable stability , 2022 .