Skip to main content
Log in

Mathematical Models of Traffic Control in Internet: New Approaches Based of TCP/AQM Schemes

  • Queueing Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Mathematical models of control of traffic in the Internet are considered. Analysis is made on approaches, models, interpretation methods, and questions arising in problems of congestion control on the basis of the interaction of TCP/AQM protocols.

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. Kelly, F., Charging and Rate Control for Elastic Traffic, Eur. Trans. Tekecom., 1997, vol. 8, pp. 33–37.

    Google Scholar 

  2. Kelly, F., Maulloo, A., and Tan, D., Rate Control in Communication Networks: Shadow Prices, Proportional Fairness and Stability, J. Oper. Res. Soc., 1998, vol. 49, no.3, pp. 237–252.

    Article  Google Scholar 

  3. Gibbens, R. and Kelly, F., Resource Pricing and the Evolution of Congestion Control, Automatica, 1999, vol. 35, pp. 1969–1985 (hthp://www.statslab.cam.ac/∼frank/evol.html).

    Article  MathSciNet  Google Scholar 

  4. Kelly, F., Mathematical Modeling of the Internet, in Mathematics Unlimited—2001 and Beyond, Engquist, B. and Schmid, W., Eds., Berlin: Springer-Verlag, 2001, pp. 685–702.

    Google Scholar 

  5. Low, S.H., A Duality Model of TCP and Queue Management Algorithms, IEEE/ACM Trans. Networking, 2003, vol. 11, no.4, pp. 525–536.

    Article  Google Scholar 

  6. Vojnovic, M. and Le Boudec, J.Y., Global TCP Modeling: The Limit Mean ODE and Its Convergence, Proc. Workshop of the Modeling of Flow and Congestion Control Mechanisms, ENS, Paris, 2000 (http://www.di.end.fr/∼mistral/tcp2.html).

    Google Scholar 

  7. Hurley, P., Le Boudec, J.Y., and Thiran, P., A Note on the Fairness of Additive Increase and Multiplicative Decrease, Proc. 16th Int. Teletraffic Congr., Edinburgh, 1999 (http://icawww.epfl.ch).

  8. Vojnovic, M. and Le Boudec, J.Y., Some Observations on Equation-Based Rate Control, Proc. 17th Int. Teletraffic Congr., Salvador da Bahia, 2001, pp. 173–184.

  9. Vojnovic, M., Boudec, J.Y., and Boutremans, C., Global Fairness of Additive-Increase and Multiplicative-Decrease with Heterogeneous Round-Trip Times, Proc. IEEE Infocom 2000, Tel Aviv, 2000, pp. 1303–1312.

  10. Athuralya, S., Lapsley, D.E., and Low, S.H., Random Early Marking for Internet Congestion Control, Proc. IEEE Globecom, 1999.

  11. Hollot, C.V. and Chait, Y., Nonlinear Stability Analysis for a Class of TCP/AQM Schemes, Proc. IEEE Conf. Decision and Control, 2001.

  12. Hollot, C.V., Misra, V., Towlsey, D., and Gong, W., A Control Theoretic Analysis of RED, Proc. IEEE Infocom, Anchorage, 2001 (http//www-net.cs.umass.edu/papers).

  13. Johari, R. and Tan, D., End-to-End Congestion Control for the Internet: Delays and Stability, IEEE/ACM Trans. on Networking, 2001, vol. 9, no.6, pp. 818–832.

    Article  Google Scholar 

  14. Kunniyur, S. and Strikant, R., Analysis and Design of an Adaptive Virtual Queue Algorithm for Active Queue Management, Proc. ACM Sigcomm, San Diego, 2001, pp. 123–134.

  15. Kunniyur, S. and Srikant, R., A Time-Scale Decomposition Approach to Adaptive ACN Marking, IEEE/ACM Trans. Automat. Control, 2002, vol. 47, no.6, pp. 882–894.

    Article  Google Scholar 

  16. Shakkottai, S., Srikant, R., and Meyn, S., Bounds on the Throughput of Congestion Controllers in the Presence of Feedback Delay, Proc. IEEE Conf. on Decision and Control, 2001.

  17. Massoulie, L., Stability of Distributed Congestion Control with Heterogeneous Feedback Delays, IEEE Trans. Automat. Control, 2002, vol. 47, pp. 895–902.

    Article  Google Scholar 

  18. Low, S.H. and Lapsley, D.E., Optimization Flow Control. I. Basic Algorithm and Convergence, IEEE/ACM Trans. on Networking, 1999, vol. 7, no.6, pp. 861–874 (http://netlab.caltech.edu).

    Article  Google Scholar 

  19. Athuraliya, S. and Low, S.H., Optimization Flow Control, II Implementation, 2000 (http://netlab.caltech.edu).

  20. Doyle, J.C., Carlson, J., Low, S.H., et al., Robustness and the Internet: Theoretical Foundations, 2002 (http://netlab.caltech.edu).

  21. Wang, C.J., Li, L., Low, S.H., and Doyle, J., Cross-Layer Optimization in TCP/IP Networks, IEEE/ACM Trans. on Networking, 2005, vol. 13 (http://netlab.caltech.edu).

  22. Low, S.H., Paganini, F., Wang, J., Adlakha, S.A., and Doyle, J.C., Dynamics of TCP/RED and a Scalable Control, Proc. IEEE Infocom, 2002 (http://netlab.caltech.edu).

  23. Low, S.H. and Srikant, R.A., Mathematical Framework for Designing a Low-Loss, Low-Delay Internet. Networks and Spatial Economics, Special Issue on Crossovers between Transportation Planning and Telecommunications, Alman, E. and Wynter, L., Eds. 2004, vol. 4, pp. 75–101 (http://netlab.caltech.edu).

  24. Low, S.H., Peterson, L., and Wang, L., Understanding Vegas: A Duality Model, J. ACM, 2002, vol. 49, no.2, pp. 207–235 (http://netlab.caltech.edu).

    Article  MathSciNet  Google Scholar 

  25. Cheng, J., Wei, D., Low, S.H., et al., FAST TCP: From Theory to Experiments, IEEE Network, 2005, vol. 19, no.1., pp. 4–11 (http://natlab.caltech.edu/fast).

    Article  Google Scholar 

  26. Jin, C., Wei, D.X., and Low, S.H., Fast TCP: Motivation, Architecture, Algorithms, Performance, Proc. IEEE Infocom, 2004 (http://netlab.caltech.edu).

  27. Low, S.H., Paganini, F., Wang, J., and Doyle, J., Linear Stability of TCP/RED and Scalable Control, Comput. Networks J., 2003, vol. 43, no.5, pp. 633–647 (http://netlab.caltech.edu).

    Article  Google Scholar 

  28. Vinnicombe, G., On the Stability of Networks Operating TCP-Like Congestion Control, Proc. 15th IFAC World Congress, Barselona, 2002 (http://www.eng.cam.ac.uk/∼gv).

  29. Low, S.H., Paganini, F., Wang, Z., and Doyle, J.C., Linear Stability of TCP/RED and a Scalable Control, Comput. Networks, 2003, vol. 43, no.5, pp. 633–647 (http://www. ElsevierComputerScience.com).

    Article  Google Scholar 

  30. Mo, J. and Walrand, J., Fair End-to-End Window-Based Congestion Control, IEEE/ACM Trans. Networking, 2000, vol. 8, no.5, pp. 556–567.

    Article  Google Scholar 

  31. Massoulie, L. and Roberts, J., Bandwidth Sharing: Objectives and Algorithms, IEEE/ACM Trans. Networking, 2002, vol. 10, no.3, pp. 320–328.

    Article  Google Scholar 

  32. Kunniyur, S. and Srikant, R., End-to-End Congestion Control: Utility Functions, Random Losses and ECN Marks, IEEE/ACM Trans. Networking, 2003, vol. 11, no.5, pp. 689–702.

    Article  Google Scholar 

  33. Paganini, F., Wang, Z., Low, S.H., and Doyle, J.C., A New TCP/AQM for Stable Operation in Fast Networks, Proc. IEEE Infocom, 2003 (http://www.ee.ucla.edu/∼paganini).

  34. Tang, A., Wang, J., and Low, S.H., Is Fair Allocation Always Inefficient? Proc. IEEE Infocom, Hong Kong, 2004.

  35. Floyd, S., High-Speed TCP for Large Congestion Windows, RFC 3649, Experimental, 2003 (http://www.icir.org/floyd/hstcp.html).

  36. Floyd, S., Ratnasamy, S., and Shenker, S., Modifying TCP’s Congestion Control for High Speeds, 2002 (http://www.icir.org/floyd).

  37. Kelly, T., Scalable TCP: Improving Performance in High-Speed Wide Area Networks, Proc. First Int. Workshop on Protocols for Fast Long-Distance Networks, Geneva, 2002 (http://www-lce.eng.cam.ac.uk/∼ctk21/scalable).

  38. Katabi, D., Handley, M., and Rohrs, C., Congestion Control for High Bandwidth-Delay Product Networks, Proc. Sigcomm, Pittsburg, 2002.

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Avtomatika i Telemekhanika, No. 8, 2005, pp. 94–107.

Original Russian Text Copyright © 2005 by Vasenin, Simonova.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vasenin, V.A., Simonova, G.I. Mathematical Models of Traffic Control in Internet: New Approaches Based of TCP/AQM Schemes. Autom Remote Control 66, 1274–1286 (2005). https://doi.org/10.1007/s10513-005-0168-0

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10513-005-0168-0

Keywords

Navigation