A Stackelberg network game with a large number of followers

Journal of Optimization Theory and Applications

Volumn 115, Issue 3, 2002, Pages 479-490

  Basar T ^a   Srikant, R ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

capacity expansion; congestion control; Leader follower game; many users (followers) limit; Nash equilibrium; networks; pricing; quality of service

Indexed keywords

COSTS; ECONOMICS; INTERNET SERVICE PROVIDERS; TRAFFIC CONGESTION;

CAPACITY EXPANSION; CONGESTION CONTROL; LEADER-FOLLOWER GAMES; MANY-USER (FOLLOWER) LIMIT; NASH EQUILIBRIA; NETWORK; NETWORK GAME; QUALITY-OF-SERVICE; SERVICE PROVIDER; STACKELBERG;

QUALITY OF SERVICE;

EID: 0036439097     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021294828483     Document Type: Article

References (18)

1. KELLY, F. P., MAULLOO, A., and TAN, D., Rate Control in Communication Networks: Shadow Prices, Proportional Fairness, and Stability, Journal of the Operations Research Society, Vol. 49, pp. 237-252, 1998.
2. GIBBENS, R. J., and KELLY, F. P., Resource Pricing and the Evolution of Congestion Control, Automatica, Vol. 35, pp. 1969-1985, 1999.
3. LOW, S. H., and LAPSLEY, D. E., Optimization Flow Control, I: Basic Algorithm and Convergence, IEEE/ACM Transactions on Networking, Vol. 35, pp. 861-875, 1999.
4. KELLY, F. P., Models for a Self-Managed Internet, Philosophical Transactions of the Royal Society, Vol. 358A, pp. 2335-2348, 2000.
5. KELLY, F. P., Mathematical Modelling of the Internet, Mathematics Unlimited: 2001 and Beyond, Edited by B. Engquist and W. Schmid, Springer Verlag, Berlin, Germany, pp. 685-702, 2001.
6. KUNNIYUR, S., and SRIKANT, R., End-to-End Congestion Control: Utility Functions, Random Losses, and ECN Marks, Proceedings of the IEEE INFOCOM, Tel Aviv, Israel, pp. 1323-1332, 2000.
7. KUNNIYUR, S., and SRIKANT, R., Analysis and Design of an Adaptive Virtual Queue Algorithm for Active Queue Management, Proceedings of the ACM SIGCOMM, San Diego, California, pp. 123-134, 2001.
8. KUNNIYUR, S., and SRIKANT, R., A Time-Scale Decomposition Approach to Adaptive ECN Marking, Proceedings of the IEEE INFOCOM, Anchorage, Alaska, pp. 1330-1339, 2001.
9. BOTVICH, D. D., and DUFFIELD, N. G., Large Deviations, Economies of Scale, and the Shape of the Loss Curve in Large Multiplexers, Queueing Systems, Vol. 20, pp. 293-320, 1995.
10. BACAR, T., and SRIKANT, R., Revenue-Maximizing Pricing and Capacity Expansion in a Many-Users Regime, Proceedings of the IEEE INFOCOM, New York, NY, pp. 1556-1563, 2002.
11. ORDA, A., ROM, R., and SHIMKIN, N., Competitive Routing in Multiuser Communication Networks, IEEE/ACM Transactions on Networking, Vol. 1, pp. 510-521, 1993.
12. KORILIS, Y., LAZAR, A., and ORDA, A., Architecting Noncooperative Networks, IEEE Journal on Selected Areas in Communications, Vol. 13, pp. 1241-1251, 1995.
13. LA, R. J., and ANANTHARAM, V., Optimal Routing Control: A Game Theoretic Approach, Proceedings of the 36th IEEE Conference on Decision and Control, San Diego, California, pp. 2910-2915, 1997.
14. ALTMAN, E., BASAR, T., and SRIKANT, R., Nash Equilibria for Combined Flow Control and Routing in Networks: Asymptotic Behavior for a Large Number of Users, IEEE Transactions on Automatic Control, Vol. 47, pp. 917-930, 2002.
15. ALTMAN, E., BASAR, T., JIMINEZ, T., and SHIMKIN, N., Competitive Routing in Networks with Polynomial Costs, IEEE Transactions on Automatic Control, Vol. 47, pp. 92-96, 2002.
16. BASAR, T., and OLSDER, G. J., Dynamic Noncooperative Game Theory, Series in Classics in Applied Mathematics, SIAM, Philadelphia, Pennsylvania, 1999.
17. CRUZ, J. B., Jr., Leader-Follower Strategies for Multilevel Systems, IEEE Transactions on Automatic Control, Vol. 23, pp. 244-254, 1978.
18. BERTSEKAS, D., Nonlinear Programming, Athena Scientific, Belmont, Massachusetts, 1995.