skip to main content
article

Stability of end-to-end algorithms for joint routing and rate control

Published:01 April 2005Publication History
Skip Abstract Section

Abstract

Dynamic multi-path routing has the potential to improve the reliability and performance of a communication network, but carries a risk. Routing needs to respond quickly to achieve the potential benefits, but not so quickly that the network is destabilized. This paper studies how rapidly routing can respond, without compromising stability.We present a sufficient condition for the local stability of end-to-end algorithms for joint routing and rate control. The network model considered allows an arbitrary interconnection of sources and resources, and heterogeneous propagation delays. The sufficient condition we present is decentralized: the responsiveness of each route is restricted by the round-trip time of that route alone, and not by the round-trip times of other routes. Our results suggest that stable, scalable load-sharing across paths, based on end-to-end measurements, can be achieved on the same rapid time-scale as rate control, namely the time-scale of round-trip times.

References

  1. M. Beckmann, C.B. McGuire and C.B. Winsten. Studies in the Economics of Transportation. Cowles Commission Monograph, Yale University Press, 1956.Google ScholarGoogle Scholar
  2. D. Bertsekas and R. Gallager. Data Networks, 2nd edition. Prentice-Hall, New Jersey, 1992. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. M. Chiang. Balancing transport and physical layers in wireless multihop networks: jointly optimal congestion control and power control. IEEE J. Sel. Areas Comm., 23:104--116, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. J. Crowcroft, R. Gibbens, F. Kelly, and S. Östring. Modelling incentives for collaboration in mobile ad hoc networks. Performance Evaluation, 57:427--439, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. C.A. Desoer and Y.T. Yang. On the generalized Nyquist stability criterion. IEEE Transactions on Automatic Control, 25:187--196, 1980.Google ScholarGoogle ScholarCross RefCross Ref
  6. S.J. Golestani. A Unified Theory of Flow Control and Routing in Data Communication Networks. PhD thesis, MIT, Dept. of Electrical Engineering and Computer Science, Cambridge, MA, 1980.Google ScholarGoogle Scholar
  7. H. Han, S. Shakkottai, C. Hollot, R. Srikant, and D. Towsley. Overlay TCP for multi-path routing and congestion control. In ENS-INRIA ARC-TCP Workshop, Paris, France, 2003.Google ScholarGoogle Scholar
  8. O.L.R. Jacobs. Introduction to Control Theory. Oxford University Press, Oxford, 1993.Google ScholarGoogle Scholar
  9. V. Jacobson. Congestion avoidance and control. Computer Communication Review 18(4): 314--329, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. R. Johari and D.K.H. Tan. End-to-end congestion control for the Internet: delays and stability. IEEE/ACM Transactions on Networking, 9:818--832, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. D.B. Johnson and D.A. Maltz. Dynamic source routing in ad hoc wireless networks. In T. Imielinski and H. Korth, editors, Mobile Computing, 153--181. Kluwer, 1996.Google ScholarGoogle Scholar
  12. F. Kelly. Fairness and stability of end-to-end congestion control. European Journal of Control, 9:159--176, 2003.Google ScholarGoogle ScholarCross RefCross Ref
  13. F.P. Kelly, A.K. Maulloo, and D.K.H. Tan. Rate control in communication networks: shadow prices, proportional fairness and stability. Journal of the Operational Research Society, 49:237--252, 1998.Google ScholarGoogle ScholarCross RefCross Ref
  14. T. Kelly. Scalable TCP: improving performance in highspeed wide area networks. Computer Communication Review, 32(2):83--91, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. T. Kelly. Engineering Flow Controls for the Internet. PhD thesis, Department of Engineering, University of Cambridge, 2004. http://www-lce.eng.cam.ac.uk/~ctk21/papers/Google ScholarGoogle Scholar
  16. L. Massoulié. Stability of distributed congestion control with heterogeneous feedback delays. IEEE Transactions on Automatic Control, 47:895--902, 2002.Google ScholarGoogle ScholarCross RefCross Ref
  17. M. Mathis, J. Semke, J. Mahdavi, and T. Ott. The macroscopic behaviour of the TCP congestion avoidance algorithm. Computer Communication Review, 27:67--82, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. J. Mo and J. Walrand. Fair end-to-end window-based congestion control. IEEE/ACM Transactions on Networking, 8:556--567, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. F. Paganini, Z. Wang, J.C. Doyle, and S.H. Low. Congestion control for high performance, stability and fairness in general networks. IEEE/ACM Transactions on Networking, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. A. Papachristodoulou, L. Li, and J.C. Doyle. Methodological frameworks for largescale network analysis and design. Computer Communication Review, 34(3):7--20, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. A. Sridharan, R. Guérin, and C. Diot. Achieving near-optimal traffic engineering solutions for current OSPF/IS-IS networks. IEEE/ACM Transactions on Networking, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. R. Srikant. The Mathematics of Internet Congestion Control. Birkhauser, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. G. Vinnicombe. On the stability of networks operating TCP-like congestion control. Proc. IFAC World Congress, Barcelona, Spain 2002.Google ScholarGoogle ScholarCross RefCross Ref
  24. G. Vinnicombe. Robust congestion control for the Internet. 2002.Google ScholarGoogle Scholar
  25. T. Voice. Delay stability results for congestion control algorithms with multi-path routing. 2004. http://www.statslab.cam.ac.uk/~tdv20Google ScholarGoogle Scholar
  26. Z. Wang and J. Crowcroft. Analysis of shortest-path routing algorithms in a dynamic network environment. Computer Communication Review, 22(2):63--71, 1992. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. J.G. Wardrop. Some theoretical aspects of road traffic research. Proceedings of the Institution of Civil Engineers, 1:325--378, 1952.Google ScholarGoogle ScholarCross RefCross Ref
  28. S. Yilmaz and I. Matta. On the scalability-performance tradeoffs in MPLS and IP routing. In Proceedings of SPIE ITCOM'2002: Scalability and Traffic Control in IP Networks, Boston, MA, 2002.Google ScholarGoogle Scholar
  29. D. Zhu, M. Gritter, and D.R. Cheriton. Feedback based routing. Computer Communication Review, 33(1):71--76, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Stability of end-to-end algorithms for joint routing and rate control

    Recommendations

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in

    Full Access

    • Published in

      cover image ACM SIGCOMM Computer Communication Review
      ACM SIGCOMM Computer Communication Review  Volume 35, Issue 2
      April 2005
      86 pages
      ISSN:0146-4833
      DOI:10.1145/1064413
      Issue’s Table of Contents

      Copyright © 2005 Authors

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 1 April 2005

      Check for updates

      Qualifiers

      • article

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader