Equilibrium of heterogeneous congestion control: Existence and uniqueness

IEEE/ACM Transactions on Networking

Volumn 15, Issue 4, 2007, Pages 824-837

  Tang, Ao ^a   Wang, Jiantao ^a   Low, Steven H ^a   Chiang, Mung ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b Princeton University   (United States)

Author keywords

Congestion control; Equilibrium analysis; Heterogeneous protocols; Optimization

Indexed keywords

CONGESTION CONTROL; CONGESTION CONTROL PROTOCOLS; EQUILIBRIUM ANALYSIS; EXISTENCE AND UNIQUENESS; HETEROGENEOUS PROTOCOLS; MAPPING FUNCTIONS; MULTI PROTOCOLS; STANDARD UTILITY MAXIMIZATIONS;

OPTIMIZATION;

COSTS;

EID: 46149107173     PISSN: 10636692     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNET.2007.893885     Document Type: Article

References (34)

1. K. Arrow and F. Hahn, General Competitive Analysis. San Francisco, CA: Holden-Day, 1971.
2. T. Basar and G. Olsder, Dynamic Noncooperative Game Theory, 2nd ed. Philadelphia, PA: SIAM, 1999.
3. G. Debreu, Theory of Value. New York: Wiley, 1959.
4. G. Debreu, "Economics with a finite set of equilibria," Econometrica, vol. 38, no. 3, pp. 387-392, May 1970.
5. G. Debreu, "Economic theory in the mathematical mode," Noble Memorial Lecture, Dec. 8, 1983.
6. E. Dierker, "Two remarks on the number of equilibria of an economy," Econometrica, vol. 40, no. 5, pp. 751-753, Sep. 1972.
7. E. Dierker and H. Dierker, "The local uniqueness of equilibria," Econometrica, vol. 40, no. 5, pp. 867-881, Sep. 1972.
8. L. Grieco and S. Mascolo, "Performance evaluation and comparison of Westwood+, New Reno, and Vegas TCP congestion control," ACM SIGCOMM Comput. Commun. Rev., vol. 34, no. 2, pp. 25-38, Apr. 2004.
9. D. Wei, C. Jin, S. H. Low, and S. Hegde, "FAST TCP: Motivation, architecture, algorithms, performance," IEEE/ACM Trans. Netw., vol. 15, no. 6, pp. 1246-1259, Dec. 2007.
10. F. Kelly, A. Maoulloo, and D. Tan, "Rate control for communication networks: Shadow prices, proportional fairness and stability," J. Oper. Res. Soc., vol. 49, pp. 237-252, 1998.
11. S. Kunniyur and R. Srikant, "End-to-end congestion control: Utility functions, random losses and ECN marks," IEEE/ACM Trans. Netw., vol. 11, no. 5, pp. 689-702, Oct. 2003.
12. K. Kurata, G. Hasegawa, and M. Murata, "Fairness comparisons between TCP Reno and TCP Vegas for future deployment of TCP Vegas," in Proc. INET, 2000 [Online]. Available: http://www.isoc.org/ inet2000/cdproceedings/2d/2d_2.htm
13. S. H. Low, "A duality model of TCP and queue management algorithms," IEEE/ACM Trans. Netw., vol. 11, no. 4, pp. 525-536, Aug. 2003.
14. S. H. Low and D. Lapsley, "Optimization flow control, I: Basic algorithm and convergence," IEEE/ACM Trans. Netw., vol. 7, no. 6, pp. 861-874, Dec. 1999.
15. S. H. Low, F. Paganini, and J. Doyle, "Internet congestion control," IEEE Control Syst. Mag., vol. 22, no. 1, pp. 28-43, Feb. 2002.
16. J. Marsden and M. Hoffman, Elementary Classical Analysis, Second ed. New York: Freeman, 1993.
17. A. Mas-Colell, The Theory of General Economic Equilibrium. A Differentiable Approach. Cambridge, U.K.: Cambridge Univ. Press, 1985.
18. A. Mas-Colell, M. Whinston, and J. Green, Microeconomic Theory. New York: Oxford Univ. Press, 1995.
19. C. Meyer, Matrix Analysis and Applied Linear Algebra. Philadelphia, PA: SIAM, 2000.
20. J. Milnor, Topology from the Differentiable Viewpoint. Charlottesville, VA: The University Press Virginia, 1972.
21. J. Mo, R. La, V. Anantharam, and J. Walrand, "Analysis and comparison of TCP Reno and Vegas," in Proc. IEEE INFOCOM, 1999, pp. 1556-1563.
22. J. Mo and J. Walrand, "Fair end-to-end window-based congestion control," IEEE/ACM Trans. Netw., vol. 8, no. 5, pp. 556-567, Oct. 2000.
23. M. Osborne and A. Rubinstein, A Course in Game Theory. Cambridge, MA: The MIT Press, 1994.
24. I. Pearce and J. Wise, "On the uniqueness of competitive equilibrium: Part I, unbounded demand," Econometrica, vol. 41, no. 5, pp. 817-828, Sep. 1973.
25. I. Pearce and J. Wise, "On the uniqueness of competitive equilibrium: Part II, bounded demand," Econometrica, vol. 42, no. 5, pp. 921-932, Sep. 1974.
26. A. Simsek, A. Ozdaglar, and D. Acemoglu, "Generalized Poincare-Hopf theorem for compact nonsmooth regions," Math. Oper. Res., vol. 32, no. 1, pp. 193-214, Feb. 2007.
27. S. Sternberg, Lectures on Differential Geometry. Englewood Cliffs, NJ: Prentice-Hall, 1964.
28. A. Tang, J. Wang, and S. H. Low, "Counter intuitive throughput behaviors in networks under end-to-end control," IEEE/ACM Trans. Netw., vol. 14, no. 3, pp. 355-368, Jun. 2006.
29. A. Tang, J. Wang, S. H. Low, and M. Chiang, "Network equilibrium of heterogeneous congestion control protocols," in Proc. IEEE INFOCOM 2005, pp. 1338-1349.
30. A. Tang, J. Wang, S. H. Low, and M. Chiang, "Equilibrium of heterogeneous congestion control protocols," Dept. Comput. Sci., California Inst. Technol., Pasadena, CSTR:2005.005, 2005.
31. A. Tang, J. Wang, S. Hedge, and S. H. Low, "Equilibrium and fairness of networks shared by TCP Reno and Vegas/FAST," Telecomm. Syst., vol. 30, no. 4, pp. 417-439, Dec. 2005.
32. A. Tang, D. Wei, S. H. Low, and M. Chiang, "Heterogeneous congestion control: Efficiency, fairness and design," in Proc. IEEE ICNP, 2006, pp. 127-136.
33. H. Varian, "A third remark on the number of equilibria of an economy," Econometrica, vol. 43, no. 5/6, pp. 985-986, Sep./Nov. 1975.
34. H. Yaiche, R. Mazumdar, and C. Rosenberg, "A game theoretic framework for bandwidth allocation and pricing in broadband networks," IEEE/ACM Trans. Netw., vol. 8, no. 3, pp. 667-678, Oct. 2000.