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.
Similar content being viewed by others
REFERENCES
Kelly, F., Charging and Rate Control for Elastic Traffic, Eur. Trans. Tekecom., 1997, vol. 8, pp. 33–37.
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.
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).
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.
Low, S.H., A Duality Model of TCP and Queue Management Algorithms, IEEE/ACM Trans. Networking, 2003, vol. 11, no.4, pp. 525–536.
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).
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).
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.
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.
Athuralya, S., Lapsley, D.E., and Low, S.H., Random Early Marking for Internet Congestion Control, Proc. IEEE Globecom, 1999.
Hollot, C.V. and Chait, Y., Nonlinear Stability Analysis for a Class of TCP/AQM Schemes, Proc. IEEE Conf. Decision and Control, 2001.
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).
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.
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.
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.
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.
Massoulie, L., Stability of Distributed Congestion Control with Heterogeneous Feedback Delays, IEEE Trans. Automat. Control, 2002, vol. 47, pp. 895–902.
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).
Athuraliya, S. and Low, S.H., Optimization Flow Control, II Implementation, 2000 (http://netlab.caltech.edu).
Doyle, J.C., Carlson, J., Low, S.H., et al., Robustness and the Internet: Theoretical Foundations, 2002 (http://netlab.caltech.edu).
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).
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).
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).
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).
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).
Jin, C., Wei, D.X., and Low, S.H., Fast TCP: Motivation, Architecture, Algorithms, Performance, Proc. IEEE Infocom, 2004 (http://netlab.caltech.edu).
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).
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).
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).
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.
Massoulie, L. and Roberts, J., Bandwidth Sharing: Objectives and Algorithms, IEEE/ACM Trans. Networking, 2002, vol. 10, no.3, pp. 320–328.
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.
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).
Tang, A., Wang, J., and Low, S.H., Is Fair Allocation Always Inefficient? Proc. IEEE Infocom, Hong Kong, 2004.
Floyd, S., High-Speed TCP for Large Congestion Windows, RFC 3649, Experimental, 2003 (http://www.icir.org/floyd/hstcp.html).
Floyd, S., Ratnasamy, S., and Shenker, S., Modifying TCP’s Congestion Control for High Speeds, 2002 (http://www.icir.org/floyd).
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).
Katabi, D., Handley, M., and Rohrs, C., Congestion Control for High Bandwidth-Delay Product Networks, Proc. Sigcomm, Pittsburg, 2002.
Author information
Authors and Affiliations
Additional information
__________
Translated from Avtomatika i Telemekhanika, No. 8, 2005, pp. 94–107.
Original Russian Text Copyright © 2005 by Vasenin, Simonova.
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10513-005-0168-0