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A global stability result for primal-dual congestion control algorithms with routing

Published: 01 July 2004 Publication History

Abstract

We prove a global stability result for a fluid approximation of a class of Internet-like communications networks operating a form of congestion control with routing. The network consists of an arbitrary interconnection of sources and links with negligible propagation delays. The model here allows for arbitrary strictly concave utility functions and the presence of dynamics at both sources and links.

References

[1]
T. Alpcan and T. Başar. A game-theoretic framework for congestion control in general topology networks. In Proceedings of 41st IEEE Conference on Decision and Control, 2002.
[2]
D. Andersen, H. Balakrishnan, M. Kaashoek, and R. Morris. The case for resilient overlay networks. In Proceedings of HotOS VIII, 2001.
[3]
E. Anderson and T. Anderson. On the stability of adaptive routing in the presence of congestion control. In Proceedings of IEEE INFOCOM, pages 948--958, 2003.
[4]
K. Arrow, L. Hurwicz, and U. Hirofumi. Studies in Linear and Non-Linear Programming. Stanford University Press, Stanford, California, 1958.
[5]
D. Bertsekas. Non-Linear Programming. Athena Scientific, Belmont, Mass, 1995.
[6]
J. Crowcroft, R. Gibbens, F. Kelly, and S. Östring. Modelling incentives for collaboration in mobile ad hoc networks. In Proceedings of WiOpt'03, 2003.
[7]
L. Fleischer. Approximating fractional multi-commodity flow independent of the number of commodities. SIAM Journal on Discrete Mathematics, 13(4):505--520, 2000.
[8]
P. Glendinning. Stability, Instability and Chaos. Cambridge University Press, Cambridge, 1994.
[9]
V. Jacobson. Congestion avoidance and control. In Proceedings of ACM SIGCOMM'88, pages 314--329, 1988.
[10]
F. Kelly. Fairness and stability of end-to-end congestion control. European Journal of Control, 9:159--176, 2003.
[11]
F. Kelly, A. Maulloo, and D. Tan. Rate control in communication networks: shadow prices, proportional fairness and stability. Journal of the Operational Research Society, 49:237--252, 1998.
[12]
S. Liu, T. Başar, and R. Srikant. Controlling the internet: A survey and some new results. In Proceedings of IEEE Conference on Decision and Control, 2003.
[13]
S. Low, F. Paganini, and J. Doyle. Internet congestion control. IEEE Control Systems Magazine, 22(1):28--43, 2002.
[14]
G. Vinnicombe. On the stability of networks operating tcp-like congestion control. In IFAC, 2002.
[15]
S. Vutukury and J. Garcia-Luna-Aceves. A simple approximation to minimum-delay routing. In Proceedings of ACM SIGCOMM '99, 1999.
[16]
J. Wen and M. Arcak. A unifying passivity framework for network flow control. In Proceedings of IEEE INFOCOM, 2003.

Cited By

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  • (2017)Improved Utility-Based Congestion Control for Delay-Constrained CommunicationIEEE/ACM Transactions on Networking10.1109/TNET.2016.258757925:1(349-362)Online publication date: 1-Feb-2017
  • (2012)Robust global stability to delays of a multi-path dual congestion control algorithmSystems & Control Letters10.1016/j.sysconle.2012.01.01361:4(535-542)Online publication date: Apr-2012
  • (2009)Transport-independent fairnessComputer Networks: The International Journal of Computer and Telecommunications Networking10.1016/j.comnet.2009.04.01153:14(2444-2457)Online publication date: 1-Sep-2009
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  1. A global stability result for primal-dual congestion control algorithms with routing

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    Published In

    cover image ACM SIGCOMM Computer Communication Review
    ACM SIGCOMM Computer Communication Review  Volume 34, Issue 3
    July 2004
    98 pages
    ISSN:0146-4833
    DOI:10.1145/1031134
    Issue’s Table of Contents

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    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 01 July 2004
    Published in SIGCOMM-CCR Volume 34, Issue 3

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    1. global stability

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    View all
    • (2017)Improved Utility-Based Congestion Control for Delay-Constrained CommunicationIEEE/ACM Transactions on Networking10.1109/TNET.2016.258757925:1(349-362)Online publication date: 1-Feb-2017
    • (2012)Robust global stability to delays of a multi-path dual congestion control algorithmSystems & Control Letters10.1016/j.sysconle.2012.01.01361:4(535-542)Online publication date: Apr-2012
    • (2009)Transport-independent fairnessComputer Networks: The International Journal of Computer and Telecommunications Networking10.1016/j.comnet.2009.04.01153:14(2444-2457)Online publication date: 1-Sep-2009
    • (2007)Stability of multi-path dual congestion control algorithmsIEEE/ACM Transactions on Networking10.1109/TNET.2007.89901115:6(1231-1239)Online publication date: 1-Dec-2007
    • (2007)Layering as Optimization Decomposition: A Mathematical Theory of Network ArchitecturesProceedings of the IEEE10.1109/JPROC.2006.88732295:1(255-312)Online publication date: Jan-2007
    • (2006)Stability of multi-path dual congestion control algorithmsProceedings of the 1st international conference on Performance evaluation methodolgies and tools10.1145/1190095.1190167(56-es)Online publication date: 11-Oct-2006
    • (2006)Optimal Capacity Sharing of Networks with Multiple Overlays200614th IEEE International Workshop on Quality of Service10.1109/IWQOS.2006.250437(72-81)Online publication date: Nov-2006
    • (2006)Congestion control with adaptive multipath routing based on optimization2006 40th Annual Conference on Information Sciences and Systems10.1109/CISS.2006.286488(333-338)Online publication date: Mar-2006
    • (2006)Joint Optimization of Scheduling and Congestion Control in Communication Networks2006 40th Annual Conference on Information Sciences and Systems10.1109/CISS.2006.286389(1572-1577)Online publication date: Mar-2006

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