Atomic resource sharing in noncooperative networks

In noncooperative networks, resources are shared among selfish users, which optimize their individual performance measure. We consider the generic and practically important case of atomic resource sharing, in which traffic bi furcation is not implemented, hence each user allocates its whole traffic t o one of the network resources. We analyze topologies of parallel resources within a game-theoretic framework and establish several fundamental proper ties. We prove the existence of and convergence to a Nash equilibrium. For a broa d class of residual capacity performance functions, an upper bound on the n umber of iterations till convergence is derived. An algorithm is presented for testing the uniqueness of the equilibrium. Sufficient conditions for ac hieving a feasible equilibrium are obtained. We consider extensions to gene ral network topologies. In particular, we show that, for a class of through put-oriented cost functions, existence of and convergence to a Nash equilib rium is guaranteed in all topologies.