A unifying passivity framework for network flow control

Network flow control regulates the traffic between sources and links based on congestion, and plays a critical role in ensuring satisfactory performance. In recent studies, global stability has been shown for several flow control schemes. By using a passivity approach, this paper presents a unifying framework which encompasses these stability results as special cases. In addition, the new approach significantly expands the current classes of stable flow controllers by augmenting the source and link update laws with passive dynamic systems. This generality offers the possibility of optimizing the controllers, for example, to improve robustness in stability and performance with respect to time delays, unmodeled flows, and capacity variation.

[1]  P. S. Bauer Dissipative Dynamical Systems: I. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[2]  G. Zames On the input-output stability of time-varying nonlinear feedback systems--Part II: Conditions involving circles in the frequency plane and sector nonlinearities , 1966 .

[3]  P. Falb,et al.  Stability Conditions for Systems with Monotone and Slope-Restricted Nonlinearities , 1968 .

[4]  G. P. Szegö,et al.  Stability theory of dynamical systems , 1970 .

[5]  J. Willems Dissipative dynamical systems part I: General theory , 1972 .

[6]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[7]  R. P. Iwens,et al.  Stability of distributed control for large flexible structures using positivity concepts , 1979 .

[8]  Gene F. Franklin,et al.  Feedback Control of Dynamic Systems , 1986 .

[9]  Petros A. Ioannou,et al.  Frequency domain conditions for strictly positive real functions , 1987 .

[10]  J. Wen Time domain and frequency domain conditions for strict positive realness , 1988 .

[11]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[12]  P. Kokotovic,et al.  A positive real condition for global stabilization of nonlinear systems , 1989 .

[13]  A. Schaft L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences 218 , 1996 .

[14]  Raj Jain Congestion Control and Traffic Management in ATM Networks: Recent Advances and a Survey , 1996, Comput. Networks ISDN Syst..

[15]  E. Ryan An Integral Invariance Principle for Differential Inclusions with Applications in Adaptive Control , 1998 .

[16]  Eitan Altman,et al.  Robust rate control for ABR sources , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

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

[18]  M. Campi,et al.  A new recursive identification algorithm for singularity free adaptive control , 1998 .

[19]  Henk Nijmeijer,et al.  System identification in communication with chaotic systems , 2000 .

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

[21]  R. SrikantCoordinated Control of Communication Networks , 1999 .

[22]  R. Srikant,et al.  A time scale decomposition approach to adaptive ECN marking , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[23]  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).

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

[25]  Christopher V. Hollot,et al.  Nonlinear stability analysis for a class of TCP/AQM networks , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

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

[27]  R. Srikant,et al.  A time-scale decomposition approach to adaptive explicit congestion notification (ECN) marking , 2002, IEEE Trans. Autom. Control..

[28]  Fernando Paganini,et al.  A global stability result in network flow control , 2002, Syst. Control. Lett..

[29]  John T. Wen,et al.  A unifying passivity framework for network flow control , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

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

[31]  Neil Genzlinger A. and Q , 2006 .

[32]  Brian D. O. Anderson,et al.  Network Analysis and Synthesis: A Modern Systems Theory Approach , 2006 .