Global Finite-Time Convergence of TCP Vegas without Feedback Information Delay

  • Choi, Joon-Young (Department of Electronic Engineering, Pusan National University) ;
  • Koo Kyung-Mo (Department of Electrical Engineering Pohang University of Science and Technology) ;
  • Lee, Jin S. (Department of Electrical Engineering Pohang University of Science and Technology) ;
  • Low Steven H. (Department of Computer Science and Electrical Engineering, California Institute of Technology)
  • Published : 2007.02.28

Abstract

We prove that TCP Vegas globally converges to its equilibrium point in finite time assuming no feedback information delay. We analyze a continuous-time TCP Vegas model with discontinuity and high nonlinearity. Using the upper right-hand derivative and applying the comparison lemma, we cope with the discontinuous signum function in the TCP Vegas model; using a change of state variables, we deal with the high nonlinearity. Although we ignore feedback information delay in analyzing the model of TCP Vegas, the simulation results illustrate that TCP Vegas in the presence of feedback information delay shows very similar dynamic trends to TCP Vegas without feedback information delay. Consequently, dynamic properties of TCP Vegas without feedback information delay can be used to estimate those of TCP Vegas in the presence of feedback information delay.

Keywords

References

  1. 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, vol. 13, no. 8, pp. 1465-1480, 1995 https://doi.org/10.1109/49.464716
  2. J. S. Ahn, P. B. Danzig, Z. Liu, and L. Yan, 'Evaluation of TCP Vegas: Emulation and experiment,” Proc. of SIGCOMM'95, 1995
  3. J. Mo, R. La, V. Anantharam, and J. Walrand, 'Analysis and comparison of TCP Reno and Vegas,' Proc. of IEEE Infocom, March 1999
  4. U. Hengartner, J. Bolliger, and Th. Gross, 'TCP Vegas revisited,' Proc. of IEEE Infocom, March 2000
  5. S. H. Low, L. L. Peterson, and L. Wang, 'Understanding TCP Vegas: A duality model,' Journal of the ACM, vol. 49, no. 2, pp. 207-235, 2002 https://doi.org/10.1145/506147.506152
  6. H. Choe and S. H. Low, 'Stabilized Vegas,' Proc. of IEEE Infocom, April 2003
  7. F. Paganini, 'A global stability result in network flow control,' System & Control Letters, vol. 46, no. 3, pp. 153-163, 2002 https://doi.org/10.1016/S0167-6911(02)00118-4
  8. S. Deb and R. Srikant, 'Global stability of congestion controllers for the internet,' IEEE Trans. on Automatic Control, vol. 48, no. 6, pp. 1055-1060, June 2003 https://doi.org/10.1109/TAC.2003.812809
  9. T. Alpcan and T. Basar, 'Global stability of an end-to-end congestion control scheme for general topology networks with delay,' Proc. of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, Dec. 2003
  10. S. Liu, T. Basar, and R. Srikant, 'Controlling the internet: A survey and some new results,' Proc. of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, Dec. 2003
  11. Z. Wang and F. Paganini, 'Global stability with time-delay of a primal-dual congestion control,' Proc. of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, Dec. 2003
  12. L. Ying, G. E. Dullerud, and R. Srikant, 'Global stability of internet congestion controllers with heterogeneous delays,' IEEE/ACM Trans. on Networking, vol. 14, no. 3, pp. 579-590, June 2006 https://doi.org/10.1109/TNET.2006.876164
  13. J. S. Lee and K. Koo, 'Global stability of TCP Vegas without network delay,' Proc. of the 43rd IEEE Conf. Decision and Control, Atlantis, Bahamas, Dec. 2004
  14. H. K. Khalil, Nonlinear Systems, 3rd edition, Prentice Hall, 2002
  15. A. F. Filippov, 'Differential equations with discontinuous right hand side,' Amer. Math. Soc. Translations, vol. 42, no. 2, pp. 199-231, 1964
  16. J. P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin Heidelberg, 1984