Existence and uniqueness of the Nash equilibrium in the non-cooperative QoS routing

References

• Altman, E., and Kameda, H. (2001), ‘Equilibria for Multi-class Routing in Multi-agent Networks’, Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, Florida, USA, December 2001, pp. 604–609.
   Google Scholar
• Altman, E., Başar, T., and Srikant, R. (1999), ‘Nash Equilibria for Combined Flow Control and Routing in Networks: Asymptotic Behaviour for a Large Number of Users’, Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, Arizona USA, December 1999, pp. 4002–4007.
   Google Scholar
• Altman, E., Başar, T., Jiménez, T., and Shimkin, N. (2002), ‘Competitive Routing in Networks with Polynomial Cost’, IEEE Transactions on Automatic Control, 2002, 47, 92–96.
   Google Scholar
• Başar , T and Olsder , GJ . 1995 . Dynamic Noncooperative Game Theory , London : Academic Press .
   Google Scholar
• Blake, S., Black, D., Carlson, M., Davies, E., Wang, Z., and Weiss, W. (1998), ‘An Architecture for Differentiated Services’. IETF RFC 2475, December.
   Google Scholar
• Chen , S and Nahrstedt , K . 1998 . An Overview of Quality of Services Routing Next-Generation High-Speed Networks: Problems and Solutions . IEEE Network , 12 : 64 – 79 .
   Web of Science ®Google Scholar
• Conforto , P and Delli Priscoli , F . 2004 . Routing and Dynamic Resource Assignment Joint Game: A Noncooperative Model for QoS Routing . International Journal of Control , 77 : 1408 – 1425 .
   Web of Science ®Google Scholar
• Conforto, P., Tocci, C., Losquadro, G., Sheriff, R.E., Chan, P.M.L., and Hu, Y.F. (2002), ‘Ubiquitous Internet in an Integrated Satellite-terrestrial Environment: The SUITED Solution’, IEEE Communication Magazine, Special Issue on Service Portability and Virtual Home Environment, 40, 98–107.
   Google Scholar
• Crawley, E., Nair, R., Rajagopalan, B., and Sandick, H. (1998), ‘A framework for QoS-based routing in the Internet’, IETF RFC 2386, August.
   Google Scholar
• El Azouzi , R and Altman , E . 2003 . Constrained Traffic Equilibrium in Routing . IEEE Transaction on Automatic Control , 48 : 1656 – 1660 .
   Web of Science ®Google Scholar
• Ferguson , P and Huston , G . 1998 . Quality of Service: Delivering QoS on the Internet and in Corporate Networks , New York : John Wiley and Sons, Inc .
   Google Scholar
• Huston, G. (2000), ‘Next Steps for the IP QoS Architecture’, IETF RFC 2990, November.
   Google Scholar
• Kameda, H., Altman, E., and Kozawa, T. (1999), ‘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’, Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, Arizona USA, December 1999.
   Google Scholar
• Kleinrock , L . 1975 . Queueing Systems–Volume I: Theory , New York : John Wiley and Sons, Inc .
   Google Scholar
• Kleinrock , L . 1976 . Queueing Systems–Volume II: Computer Applications , New York : John Wiley and Sons, Inc .
   Google Scholar
• Korilis , YA , Lazar , AA and Orda , A . 1997 . Capacity Allocation Under Non-cooperative Routing . IEEE Transactions on Automatic Control , 42 : 309 – 325 .
   Web of Science ®Google Scholar
• Lazar, A., Orda., A., and Pendarakis, D.E. (1995), ‘Virtual Path Bandwidth Allocation in Multi-user Networks’, Proceedings of the IEEE INFOCOM’95, Boston, USA, April, pp. 312–320.
   Google Scholar
• MacKie-Mason , JK and Varian , HR . 1995 . Pricing Congestible Network Resources . IEEE Journal on Selected Areas in Communication , 13 : 1141 – 1149 .
   Web of Science ®Google Scholar
• Orda , A , Rom , R and Shimkin , N . 1993 . Competitive Routing in Multi-user Communication Networks . IEEE/ACM Transactions on Networking , 1 : 510 – 521 .
   Web of Science ®Google Scholar
• Rosen , JB . 1965 . Existence and Uniqueness of Equilibrium Points for Concave N-Person Games . Econometrica , 33 : 520 – 534 .
   Web of Science ®Google Scholar
• Xiao , X and Ni , LM . 1999 . Internet QoS: A Big Picture . IEEE Network , 13 : 8 – 18 .
   Web of Science ®Google Scholar