Abstract
We investigate the interaction between Transmission Control Protocol (TCP) and an Active Queue Management (AQM) router, that are designed to control congestion in the Internet. TCP controls the sending rate with which the data is injected into the network and AQM generates control signals based on the congestion level. For a given TCP version, we define the optimal strategy for the AQM router as a solution of a nonlinear periodic optimization problem, and we find this solution using a linear programming approach. We show that depending on the choice of the utility function for the sending rate, the optimal control is either periodic or steady state. Main attention is paid to a problem with a sigmoidal utility function, in which the evolution of the optimal sending rate resembles a “saw-tooth” behavior of the “instantaneous” TCP sending rate.
The work was supported by the Australian Research Council Discovery-Project Grants DP0346099, DP0664330, Linkage International Grant LX0560049 and France Telecom R&D Grant “Modélisation et Gestion du Trafic réseaux Internet” no. 42937433.
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Avrachenkov, K., Ayesta, U., Piunovsky, A.: Optimal Choice of the Buffer Size in the Internet Routers. In: Proceedings of IEEE CDC-ECC (2005)
Avrachenkov, K., Finlay, L., Gaitsgory, V.: TCP-AQM Interaction: Periodic Optimization via Linear Programming. In: Yan, H., Yin, G., Zhang, Q. (eds.) Control Theory Applications in Financial Engineering and Manufacturing. Fred Hillier’s International Series in Operations Research and Management Sciences. Springer (Kluwer), Heidelberg (to appear)
Allman, M., Paxson, V., Stevens, W.: TCP congestion control, RFC 2581 (April 1999), Available at: http://www.ietf.org/rfc/rfc2581.txt
Christiansen, M., Jeffay, K., Ott, D., Donelson Smith, F.: Tuning RED for Web Traffic. IEEE/ACM Trans. on Networking, 9(3), 249–264 (June 2001); An earlier version appeared in Proc. of ACM SIGCOMM (2000)
Colonius, F.: Optimal Periodic Control. Lecture Notes in Mathematics. Springer, Berlin (1988)
Fazel, M., Chiang, M.: Network Utility Maximization with Nonconcave Utilities Using Sum-of-Squares Method. In: Proceedings of IEEE CDC-ECC (2005)
Floyd, S., Jacobson, V.: Random Early Detection Gateways for Congestion Avoidance. IEEE/ACM Trans. on Networking 1(4), 397–413 (1993)
Gaitsgory, V.: Suboptimization of Singularly Perturbed Control Problems. SIAM J. Control and Optimization 30(5), 1228–1240 (1992)
Gaitsgory, V., Rossomakhine, S.: Linear Programming Approach to Deterministic Long Run Average Problems of Optimal Control. SIAM J. Control and Optimization 44(6), 2006–2037 (2005/2006)
Jacobson, V.: Congestion avoidance and control. In: ACM SIGCOMM 1988 (August 1988)
Kelly, T.: Scalable TCP: Improving performance in highspeed wide area networks. Computer Comm. Review 33(2), 83–91 (2003)
Lee, J.-W., Mazumdar, R., Shroff, N.: Non-Convex Optimization and Rate Control for Multi-Class Services in the Internet. IEEE/ACM Trans. on Networking 13(4) (2005)
Low, S., Paganini, F., Doyle, J.: Internet Congestion Control. IEEE Control Systems Magazine 22(1), 28–43 (2002)
Misra, V., Gong, W., Towsley, D.: A Fluid-based Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED. In: Proceedings of ACM SIGCOMM (2000)
May, M., Bolot, J., Diot, C., Lyles, B.: Reasons Not to Deploy RED. In: Proceedings of 7th International Workshop on Quality of Service (IWQoS 1999), London, UK (June 1999)
Postel, J.: User Datagram Protocol. RFC 768 (August 1980), Available at: http://www.ietf.org/rfc/rfc0768.txt
Ramakrishnan, K., Floyd, S., Black, D.: The Addition of Explicit Congestion Notification (ECN) to IP. RFC 3168 (September 2001), Available at: http://www.ietf.org/rfc/rfc3168.txt
Shenker, S.: Fundamental Design Issues for the Future Internet. IEEE J. Selected Areas Commun. 13(7), 1176–1188 (1995)
Srikant, R.: The Mathematics of Internet Congestion Control. Birkhaüser, Boston (2004)
ILOG CPLEX, http://ilog.com/products/cplex/
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Avrachenkov, K., Finlay, L., Gaitsgory, V. (2006). Analysis of TCP-AQM Interaction Via Periodic Optimization and Linear Programming: The Case of Sigmoidal Utility Function. In: Koucheryavy, Y., Harju, J., Iversen, V.B. (eds) Next Generation Teletraffic and Wired/Wireless Advanced Networking. NEW2AN 2006. Lecture Notes in Computer Science, vol 4003. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759355_47
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DOI: https://doi.org/10.1007/11759355_47
Publisher Name: Springer, Berlin, Heidelberg
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