Distributed iterative optimal resource allocation with concurrent updates of routing and flow control variables

ABSTRACT

Consider a set of active elastic sessions over a network. Session traffic is routed at each hop (potentially through multiple network paths) based only on its destination. Each session is associated with a concave increasing utility function of its transfer rate. The transfer rates of all sessions and the routing policy define the operating point of the network.We construct a metric f of the goodness of this operating point. f is an increasing function of the session utilities and a decreasing function of the extent of congestion in the network.We define"good" operating points as those that maximizef, subject to the capacity constraints in the network. This paper presents a distributed, iterative algorithm for adapting the session rates and the routing policy across the network so as to converge asymptotically to the set of "good" operating points. The algorithm updates session rates and routing variables concurrently and is, therefore, amenable to distributed online implementation. The convergence of the concurrent update scheme is proved rigorously.

REFERENCES

• 1: F. Kelly, A. Maulloo, and D. Tan, "Rate control in communication networks: Shadow prices, proportional fairness and stability," J. Oper. Res. Soc., vol. 49, no. 3, pp. 237-252, 1998.
• 2: Steven H. Low , David E. Lapsley, Optimization flow control—I: basic algorithm and convergence, IEEE/ACM Transactions on Networking (TON), v.7 n.6, p.861-874, Dec. 1999 [doi>10.1109/90.811451]
• 3: K. Kar, S. Sarkar, and L. Tassiulas, "Optimization based rate control for multipath sessions," Inst. for Syst. Res., Univ. of Maryland, Tech. Rep. No. 2001-1, 2001.
• 4: X. Lin and N. B. Shroff, "Utility maximization for communication networks with multi-path routing," IEEE Trans. Automat. Control, vol. 51, no. 5, pp. 766-781, May 2006.
• 5: Dimitri Bertsekas , Robert Gallager, Data networks, Prentice-Hall, Inc., Upper Saddle River, NJ, 1987
• 6: R. G. Gallager, "A minimum delay routing algorithm using distributed computation," IEEE Trans. Commun., vol. COM-25, no. 1, pp. 73-85, Jan. 1977.
• 7: V. S. Borkar and P. R. Kumar, "Dynamic Cesaro-Wardrop equilibration in networks," IEEE Trans. Automat. Control, vol. 48, no. 3, pp. 382-396, Mar. 2003.
• 8: Xin Wang , Koushik Kar, Cross-layer rate control for end-to-end proportional fairness in wireless networks with random access, Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing, May 25-27, 2005, Urbana-Champaign, IL, USA [doi>10.1145/1062689.1062710]
• 9: F. Paganini, "Congestion control with adaptive multipath routing based on optimization," in Proc. 40th Conf. Inf. Sci. Syst. (CISS 2006), Princeton, NJ, Mar. 2006, pp. 333-338.
• 10: J. Pongsajapan and S. H. Low, "Reverse engineering TCP/IP-like networks using delay-sensitive utility functions," in Proc. IEEE INFOCOM, Anchorage, Alaska, May 2007, pp. 418-426.
• 11: Haïkel Yaïche , Ravi R. Mazumdar , Catherine Rosenberg, A game theoretic framework for bandwidth allocation and pricing in broadband networks, IEEE/ACM Transactions on Networking (TON), v.8 n.5, p.667-678, Oct. 2000 [doi>10.1109/90.879352]
• 12: Multipath Optimization Flow Control, Proceedings of the 8th IEEE International Conference on Networks, p.39, September 05-08, 2000
• 13: Dimitri P. Bertsekas , John N. Tsitsiklis, Parallel and distributed computation: numerical methods, Prentice-Hall, Inc., Upper Saddle River, NJ, 1989
• 14: Alexander L. Stolyar, Maximizing Queueing Network Utility Subject to Stability: Greedy Primal-Dual Algorithm, Queueing Systems: Theory and Applications, v.50 n.4, p.401-457, August 2005 [doi>10.1007/s11134-005-1450-0]
• 15: A. Eryilmaz and R. Srikant, "Joint congestion control, routing, and MAC for stability and fairness in wireless networks," IEEE J. Sel. Areas Commun., vol. 24, no. 8, pp. 1514-1524, Aug. 2006.
• 16: Leonidas Georgiadis , Mike Neely , Leandros Tassiulas, Resource Allocation and Cross Layer Control in Wireless Networks (Foundations and Trends in Networking, V. 1, No. 1), Now Publishers Inc., Hanover, MA, 2006
• 17: Vivek S. Borkar, Stochastic approximation with two time scales, Systems & Control Letters, v.29 n.5, p.291-294, Feb. 1997 [doi>10.1016/S0167-6911(97)90015-3]
• 18: J. Zhang, D. Zheng, and M. Chiang, "The impact of stochastic noisy feedback on distributed network utility maximization," IEEE Trans. Inf. Theory, vol. 54, no. 2, pp. 645-665, Feb. 2008.
• 19: M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear Programming: Theory and Algorithms. New York: Wiley, 1993.
• 20: P. Dupuis and A. Nagurney, "Dynamical systems and variational inequalities," Ann. Oper. Res., vol. 55, pp. 9-42, 1993.
• 21: H. K. Khalil, Nonlinear Systems. Englewood Cliffs, NJ: Prentice-Hall, 2002.
• 22: H. J. Kushner and G. G. Yin, Stochastic Approximation and Recursive Algorithms and Applications. New York: Springer, 1997.
• 23: V. S. Borkar, Stochastic Approximation: A Dynamical Systems Viewpoint . New Delhi, India: Hindustan Book Agency and Cambridge, U.K.: Cambridge Univ. Press, 2008.
• 24: W. Rudin, Principles of Mathematical Analysis. New York: Mc-Graw-Hill, 1976.

INDEX TERMS

Primary Classification:
  C. Computer Systems Organization
  C.2 COMPUTER-COMMUNICATION NETWORKS
      C.2.2 Network Protocols
          Subjects: Routing protocols

Additional Classification:
  C. Computer Systems Organization
  C.2 COMPUTER-COMMUNICATION NETWORKS
      C.2.3 Network Operations
          Subjects: Network management
  C.4 PERFORMANCE OF SYSTEMS
      Subjects: Performance attributes

  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Sequencing and scheduling

General Terms:
Algorithms, Design, Management, Performance

Keywords:
multipath routing, optimal rate control, optimal routing, two timescale iterations