Equilibria for multiclass routing problems in multi-agent networks

Annals of the International Society of Dynamic Games

Volumn 7, Issue , 2005, Pages 343-367

  Altman, Eitan ^a   Kameda, Hisao ^b  

^a INRIA   (France)

^b UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

Game theory; Networks; Routing

Indexed keywords

EID: 85012063753     PISSN: 24740179     EISSN: 24740187     Source Type: Book Series    
DOI: 10.1007/0-8176-4429-6_20     Document Type: Chapter

References (29)

1. Altman E., Başar E., Jiménez T. and Shimkin N., “Competitive routing in networks with polynomial cost”, IEEE Trans. on Automatic Control, 47, 92– 96, 2002.
2. Baskett F., Chandy K. M., Muntz R. R. and Palacios F., “Open, closed, and mixed networks of queues with different classes of customers”, J. ACM. 22, 248–260, 1975.
3. Bennett L. D., “The existence of equivalent mathematical programs for certain mixed equilibrium traffic assignment problems”, European J. of Operations Research, 71, 177–187, 1993.
4. Braess D., “Über ein Paradoxen aus der Verkehrsplanung”, Unternehmensforschung 12, 258–268, 1968.
5. Cantor D. G. and Gerla M., “Optimal routing in a packet-switched computer network,” IEEE Trans. Computers C-23, 1062–1069, 1973.
6. Dafermos S., “The traffic assignment problem for multiclass-user transportation networks”, Transportation Sci. 6, 73–87, 1972.
7. Dafermos S. and Sparrow F. T., “The traffic assignment problem for a general network”, Journal of Research of the National Bureau of Standards-B. Math. Sci., 73B, No. 2, 91–118, 1969.
8. Fratta L., Gerla M. and Kleinrock L., “The flow deviation method—an approach to the store-and-forward communication network design”, Networks 3, 97–133, 1973.
9. Gupta P. and Kumar P. R., “A system and traffic dependent adaptive routing algorithm for ad hoc networks”, Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, Florida, USA, Dec. 1998.
10. Haurie A. and Marcott P., “On the relationship between Nash-Cournot and Wardrop equilibria”, Networks 15, 295–308, 1985.
11. Kameda H., Kozawa T. and Li J., “Anomalous relations among various performance objectives in distributed computer systems”, Proc. World Congress on Systems Simulation, 459–465, Sept, 1997.
12. Kameda H., Li J., Kim C. and Zhang Y., Optimal Load Balancing in Distributed Computer Systems, Springer, London, 1997.
13. Kameda H. and Zhang Y., “Uniqueness of the solution for optimal static routing in open BCMP queueing networks”, Math. Comput. Modeling 22, No. 10–12, 119–130, 1995.
14. Kleinrock L., Queueing Systems, Vol 2, Wiley, New York, 1976.
15. Korilis, Y. A., Lazar, A. A. and Orda, A., “Architecting noncooperative net-works”, IEEE Journal of Selected Areas of Communications, 13, 1241–1251, 1995.
16. Kameda H., Altman E. and Kozawa T., “A case where a paradox like Braess’s occurs in the Nash equilibrium but does not occur in the Wardrop equilibrium – a situation of load balancing in distributed computer systems”, Proc. of the 38th IEEE Conference on Decision and Control, Phoenix, Arizona, USA, Dec. 1999.
17. Kameda H., Altman E., Kozawa T. and Hosokawa Y., “Braess-like paradoxes of Nash equilibria for load balancing in distributed computer systems”, IEEE Trans. on Automatic Control, 45, No. 9, 1687–1691, 2000.
18. Kelly F. P., Reversibility and Stochastic Networks, John Wiley & Sons, New York (1979).
19. La R. J. and Anantharam V., “Optimal routing control: game theoretic approach”, Proc. of the 36th IEEE Conference on Decision and Control, San Diego, California, Dec. 1997.
20. Li J. and Kameda H., “Load balancing problems for multiclass jobs in dis-tributed/parallel computer systems,” IEEE Trans. Comp. 47, No. 3, 1998, pp. 322–1998.
21. Monderer D. and Shapley L. S., “Potential games”, Games and Econ. Behavior, 14, 124–143, 1996.
22. Orda A., Rom R. and Shimkin N., “Competitive routing in multi-user envi-ronments”, IEEE/ACM Trans. on Networking, 1, No. 5, 510–521, 1993.
23. Patriksson M. The Traffic Assignment Problem: Models and Methods VSP BV, P.O. Box 346, 3700 AH Zeist, The Netherlands, 1994.
24. Sandholm W. H., “Potential games with continuous player sets”, Journal of Economic Theory, 97, No. 1, 81–108, 2001.
25. Shapiro J. F., Mathematical Programming, Structures and Algorithms, J. Wiley, New York, 1979.
26. Stallings W., High Speed Networks: TCP/IP and ATM design principles. Upper Saddle River, NJ, USA: Prentice-Hall, Inc., 1998.
27. Tantawi A. N. and Towsley D., “A general model for optimal static load balancing in star network configurations”, Proc. of PERFORMANCE’ 84, North-Holland, New York, 277–291 (1984).
28. Tantawi A. N. and Towsley D., “Optimal static load balancing in distributed computer systems”, J. ACM 32, 445–465, 1985.
29. Wardrop J. G., “Some theoretic aspects of road traffic research”, Proc. Inst. Civ. Eng. Part 2, 1, 325–378, 1952.