Competitive routing in multicast communications

We consider competitive routing in multicast networks from a noncooperative game theoretical perspective. There are N users sharing a network, and each has to send a quantity of packets to a different set of addressees (each address must receive the same packets). To do this the user has only to send one copy of a packet, the network making the duplications of the packets at appropriate nodes (depending on the chosen trees). The routing choice of a user is how to split its flow between different multicast trees. We present different criteria for optimization of this type of game. We treat two specific networks and establish the uniqueness of the Nash equilibrium in these networks, as well as the uniqueness of link utilization at Nash equilibria for specific cost functions in networks with general topology. We also present a result for convergence to equilibria from an initial nonequilibrium state. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 46(1), 22–35 2005

[1]  J. Goodman.  Note on Existence and Uniqueness of Equilibrium Points for Concave N-Person Games , 1965 .

[2]  Ariel Orda,et al.  Architecting noncooperative networks , 1995, Eighteenth Convention of Electrical and Electronics Engineers in Israel.

[3]  Hisao Kameda,et al.  Mixed equilibrium (ME) for multiclass routing games , 2002, IEEE Trans. Autom. Control..

[4]  Hiroshi Yasuda,et al.  Variable bit-rate coding of video signals for ATM networks , 1989, IEEE J. Sel. Areas Commun..

[5]  Richard J. La,et al.  Optimal routing control: game theoretic approach , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[6]  Martin Vetterli,et al.  Receiver-driven layered multicast , 1996, SIGCOMM 1996.

[7]  Shantayanan Devarajan,et al.  A note of network equilibrium and noncooperative games , 1981 .

[8]  Stella C. Dafermos,et al.  Traffic assignment problem for a general network , 1969 .

[9]  J. Neumann,et al.  SOLUTIONS OF GAMES BY DIFFERENTIAL EQUATIONS , 1950 .

[10]  William H. Sandholm,et al.  Potential Games with Continuous Player Sets , 2001, J. Econ. Theory.

[11]  T. Bially,et al.  A Technique for Adaptive Voice Flow Control in Integrated Packet Networks , 1980, IEEE Trans. Commun..

[12]  Alain Haurie,et al.  On the relationship between Nash - Cournot and Wardrop equilibria , 1983, Networks.

[13]  Deborah Estrin,et al.  Pricing in computer networks: motivation, formulation, and example , 1993, TNET.

[14]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[15]  Ariel Orda,et al.  Competitive routing in multiuser communication networks , 1993, TNET.

[16]  A. Nagurney,et al.  Projected Dynamical Systems and Variational Inequalities with Applications , 1995 .

[17]  T. Koopmans,et al.  Studies in the Economics of Transportation. , 1956 .

[18]  Mike Smith,et al.  The existence, uniqueness and stability of traffic equilibria , 1979 .

[19]  Piyush Gupta,et al.  A system and traffic dependent adaptive routing algorithm for ad hoc networks , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[20]  Stella Dafermos,et al.  Traffic Equilibrium and Variational Inequalities , 1980 .

[21]  Eitan Altman,et al.  Uniqueness of solutions for optimal static routing in multi-class open networks , 1998 .

[22]  Masahiro Wada,et al.  Selective recovery of video packet loss using error concealment , 1989, IEEE J. Sel. Areas Commun..

[23]  Eitan Altman,et al.  Equilibria for Multiclass Routing Problems in Multi-Agent Networks , 2005 .

[24]  David D. Yao,et al.  S-modular games, with queueing applications , 1995, Queueing Syst. Theory Appl..