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LBMP: A Logarithm-Barrier-Based Multipath Protocol for Internet Traffic Management
March 2011 (vol. 22 no. 3)
pp. 476-488
Ke Xu, Tsinghua University, Beijing
Hongying Liu, Beijing University of Aeronautics and Astronautics, Beijing
Jiangchuan Liu, Simon Fraser University, Burnaby
Jixiu Zhang, Peking University, Beijing
Traffic management is the adaptation of source rates and routing to efficiently utilize network resources. Recently, the complicated interactions between different Internet traffic management modules have been elegantly modeled by distributed primal-dual utility maximization, which sheds new light for developing effective management protocols. For single-path routing with given routes, the dual is a strictly concave network optimization problem. Unfortunately, the general form of multipath utility optimization is not strictly concave, making its solution quite unstable. Decomposition-based techniques like TRaffic-management Using Multipath Protocol (TRUMP) alleviates the instability, but their convergence is not guaranteed, nor is their optimality. They are also inflexible in differentiating the control at different links. In this paper, we address the above issues through a novel logarithm-barrier-based approach. Our approach jointly considers user utility and routing/congestion control. It translates the multipath utility maximization into a sequence of unconstrained optimization problems, with infinite logarithm barriers being deployed at the constraint boundary. We demonstrate that setting up barriers is much simpler than choosing traditional cost functions and, more importantly, it makes optimal solution achievable. We further demonstrate a distributed implementation, together with the design of a practical Logarithm Barrier-based-Multipath Protocol (LBMP). We evaluate the performance of LBMP through both numerical analysis and packet-level simulations. The results show that LBMP achieves high throughput and fast convergence over diverse representative network topologies. Such performance is comparable to TRUMP, and is often better. Moreover, LBMP is flexible in differentiating the control at different links, and its optimality and convergence are theoretically guaranteed.

[1] S. Athuraliya and S.H. Low, "Optimization Flow Control with Newton-Like Algorithm," J. Telecomm. Systems, vol. 15, pp. 345-358, 2000.
[2] D.P. Bertsekas, Nonlinear Programming, second ed. Athena Scientific, 1999.
[3] M. Chiang, "Balancing Transport and Physical Layer in Wireless Multihop Networks: Jointly Optimal Congestion Control and Power Control," IEEE J. Selected Areas in Comm., vol. 23, no. 1, pp. 104-116, Jan. 2005.
[4] M. Chiang, S.H. Low, A.R. Calderbank, and J.C. Doyle, "Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures," Proc. IEEE, vol. 95, no. 1, pp. 255-312, Jan. 2007.
[5] A.L.H. Chow, L. Golubchik, J.C.S. Lui, and W.-J. Lee, "Multipath Streaming: Optimization of Load Distribution," Performance Evaluation, vol. 62, no. 4, pp. 417-438, 2005.
[6] B. Fortz and M. Thorup, "Optimizing OSPF Weights in a Changing World," IEEE J. Selected Areas in Comm., vol. 20, no. 4, pp. 756-767, May 2002.
[7] H. Han, S. Shakkottai, C.V. Hollot, R. Srikant, and D. Towsley, "Multi-Path TCP: A Joint Congestion Control and Routing Scheme to Exploit Path Diversity on the Internet," IEEE/ACM Trans. Networking, vol. 14, no. 6, pp. 1260-1271, Dec. 2006.
[8] J. He, M. Bresler, M. Chiang, and J. Reford, "Towards Robust Multi-Layer Traffic Engineering Optimization of Congestion Control and Routing," IEEE J. Selected Areas in Comm., vol. 25, no. 5, pp. 868-880, June 2007.
[9] J. He, M. Suchara, and M. Chiang, "Rethinking Internet Traffic Management: From Multiple Decompositions to a Practical Protocol," Proc. ACM Int'l Conf. Emerging Networking Experiments and Technologies (CoNEXT '07), 2007.
[10] J. He, M. Suchara, M. Bresler, J. Rexford, and M. Chiang, "From Multiple Decompositions to TRUMP: Traffic Management Using Multipath Protocol," to be published in Elsevier Computer Networks.
[11] J. He and J. Rexford, "Towards Internet-Wide Multipath Routing," IEEE Network Magazine, vol. 22, no. 2, pp. 16-21, Mar. 2008.
[12] F. Kelly, A. Maulloo, and D. Tan, "Rate Control for Communication Networks: Shadow Prices, Proportional Fairness and Stability," J. Operational Research Soc., vol. 49, no. 3, pp. 237-252, 1998.
[13] F. Kelly, The Mathematics of Traffic in Network. Princeton Univ. Press, 2005.
[14] F. Kelly and T. Voice, "Stability of End-to-End Algorithms for Joint Routing and Rate Control," ACM SIGCOMM Computer Comm. Rev., vol. 35, no. 2, pp. 5-12, 2005.
[15] S. Low, L. Peterson, and L. Wang, "Understanding Vegas: A Duality Model," J. ACM, vol. 49, no. 2, pp. 207-235, 2002.
[16] S. Low, "A Duality Model of TCP and Queue Management Algorithms," IEEE/ACM Trans. Networking, vol. 11, no. 4, pp. 525-536, Aug. 2003.
[17] S.C.M. Lee, J. Jiang, D.-M. Chiu, and J.C.S. Lui, "Interaction of ISPs: Distributed Resource Allocation and Revenue Maximization," IEEE Trans. Parallel and Distributed Systems, vol. 19, no. 2, pp. 204-218, Feb. 2008.
[18] X. Lin and N. Shroff, "Utility Maximization for Communication Networks with Multipath Routing," IEEE Trans. Automatic Control, vol. 51, no. 5, pp. 766-781, May 2006.
[19] J. Mo and J. Walrand, "Fair End-to-End Window-Based Congestion Control," IEEE/ACM Trans. Networking, vol. 8, no. 5, pp. 556-567, Oct. 2000.
[20] R. Srikant, The Mathematics of Internet Congestion Control. Birkhauser, 2004.
[21] D. Palomar and M. Chiang, "Alternative Decompositions for Distributed Maximization of Network Utility: Framework and Applications," IEEE Trans. Automatic Control, vol. 52, no. 12, pp. 2254-2269, Dec. 2007.
[22] T. Voice, "Stability of Multipath Dual Congestion Control Algorithm," IEEE/ACM Trans. Networking, vol. 15, no. 6, pp. 1231-1239, Dec. 2007.
[23] J. Wang, L. Li, S. Low, and J. Doyle, "Can TCP and Shortest-Path Routing Maximize Utility," Proc. IEEE INFOCOM, pp. 2049-2056, Apr. 2003.
[24] J. Wang, D. Wei, and S. Low, "Cross-Layer Optimization in TCP/IP Networks," IEEE/ACM Trans. Networking, vol. 13, no. 3, pp. 568-582, June 2005.
[25] D. Wei, C. Jin, S. Low, and S. Hegde, "FAST TCP: Motivation, Architecture, Algorithms, Performance," IEEE/ACM Trans. Networking, vol. 14, no. 6, pp. 1246-1259, Dec. 2006.
[26] Abilene Backbone. http://www.internet2.edunetwork/, 2010.
[27] China Education and Research Network. http://www.edu.cn/english_1369index.shtml , 2010.

Index Terms:
Traffic management, network utility maximization, multipath routing, logarithm barrier.
Citation:
Ke Xu, Hongying Liu, Jiangchuan Liu, Jixiu Zhang, "LBMP: A Logarithm-Barrier-Based Multipath Protocol for Internet Traffic Management," IEEE Transactions on Parallel and Distributed Systems, vol. 22, no. 3, pp. 476-488, March 2011, doi:10.1109/TPDS.2010.95
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