Skip to main content
Log in

Optimization flow control with Newton‐like algorithm

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

We proposed earlier an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. The control mechanism is derived as a gradient projection algorithm to solve the dual problem. In this paper we extend the algorithm to a scaled gradient projection. The diagonal scaling matrix approximates the diagonal terms of the Hessian and can be computed at individual links using the same information required by the unscaled algorithm. We prove the convergence of the scaled algorithm and present simulation results that illustrate its superiority to the unscaled algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Athuraliya, D. Lapsley and S. Low, An enhanced random early marking algorithm for Internet flow control, in: Proc. of IEEE Infocom, March 2000.

  2. S. Athuraliya and S. Low, Optimization flow control, II: REM, submitted for publication (April 2000), http://www.ee.mu.oz.au/staff/slow/research/.

  3. L. Benmohamed and S.M. Meerkov, Feedback control of congestion in store-and-forward networks: The case of a single congested node, IEEE/ACM Transactions on Networking 1(6) (December 1993) 693–707.

    Article  Google Scholar 

  4. D. Bertsekas, Nonlinear Programming (Athena Scientific, 1995).

  5. D.P. Bertsekas and J.N. Tsitsiklis, Parallel and Distributed Computation (Prentice-Hall, Englewood Cliffs, NJ, 1989).

    Google Scholar 

  6. F. Bonomi, D. Mitra and J.B. Seery, Adaptive algorithms for feedback-based flow control in highspeed wide-area ATM networks, IEEE Journal on Selected Areas in Communications 13(7) (September 1995) 1267–1283.

    Article  Google Scholar 

  7. L.S. Brakmo and L.L. Peterson, TCP Vegas: End to end congestion avoidance on a global Internet, IEEE Journal on Selected Areas in Communications 13(8) (October 1995).

  8. S. Chong, R. Nagarajan and Y.-T. Wang, Designing stable ABR flow control with rate feedback and open loop control: First order control case, Performance Evaluation 34(4) (December 1998) 189–206.

    Article  Google Scholar 

  9. C. Courcoubetis, V.A. Siris and G.D. Stamoulis, Integration of pricing and flow control for ABR services in ATM networks, in: Proc. of Globecom'96, November 1996.

  10. S. Floyd, TCP and explicit congestion notification, ACM Computer Communication Review 24(5) (October 1994).

  11. S. Floyd and V. Jacobson, Random early detection gateways for congestion avoidance, IEEE/ACM Transactions on Networking 1(4) (August 1993) 397–413.

    Article  Google Scholar 

  12. R.G. Gallager and S.J. Golestani, Flow control and routing algorithms for data networks, in: Proc. of the 5th Internat. Conf. on Computing and Communications, 1980, pp. 779–784.

  13. J. Golestani and S. Bhattacharyya, End-to-end congestion control for the Internet: A global optimization framework, in: Proc. of Internat. Conf. on Network Protocols (ICNP), October 1998.

  14. V. Jacobson, Congestion avoidance and control, in: Proc. of SIGCOMM'88, ACM, New York, August 1988; an updated version is available via ftp://ftp.ee.lbl.gov/papers/ congavoid.ps.Z.

    Google Scholar 

  15. F.P. Kelly, Charging and rate control for elastic traffic, European Transactions on Telecommunications 8 (1997) 33–37; http://www.statslab.cam.ac.uk/~frank/elastic.html.

    Article  Google Scholar 

  16. F.P. Kelly, A. Maulloo and D. Tan, Rate control for communication networks: Shadow prices, proportional fairness and stability, Journal of Operations Research Society 49(3) (March 1998) 237–252.

    Article  Google Scholar 

  17. D.E. Lapsley and S.H. Low, An optimization approach to ABR control, in: Proc. of the ICC, June 1998.

  18. D.E. Lapsley and S.H. Low, Random early marking for Internet congestion control, in: Proc. of IEEE Globecom'99, December 1999.

  19. S. Low, L. Peterson and L. Wang, Understanding Vegas: theory and practice, submitted for publication (February 2000); http://www.ee.mu.oz.au/staff/slow/research/.

  20. S.H. Low and D.E. Lapsley, Optimization flow control, I: Basic algorithm and convergence, IEEE/ACM Transactions on Networking 7(6) (December 1999); http://www.ee.mu.oz.au/ staff/slow/research/.

  21. D.G. Luenberger, Optimization by Vector Space Methods (Wiley, New York, 1968).

    Google Scholar 

  22. D.G. Luenberger, Linear and Nonlinear Programming, 2nd ed. (Addison-Wesley, Reading, MA, 1984).

    Google Scholar 

  23. K.K. Ramakrishnan and S. Floyd, A proposal to add Explicit Congestion Notification (ECN) to IP, Internet draft draft-kksjf-ecn-01.txt, July 1998.

  24. K.K. Ramakrishnan and R. Jain, A binary feedback scheme for congestion avoidance in computer networks with a connectionless network layer, in: Proc. of SIGCOMM'88, ACM, New York, August 1988.

    Google Scholar 

  25. G. Ramamurthy and A. Kolarov, Application of control theory for the design of closed loop rate control for abr service, in: Proc. of ITC 15, 1997, pp. 751–760.

  26. J.N. Tsitsiklis and D.P. Bertsekas, Distributed asynchronous optimal routing in data networks, IEEE Transactions on Automatic Control 31(4) (April 1986) 325–332.

    Article  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Athuraliya, S., Low, S.H. Optimization flow control with Newton‐like algorithm. Telecommunication Systems 15, 345–358 (2000). https://doi.org/10.1023/A:1019155231293

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1019155231293

Keywords

Navigation