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 bifurcation is not implemented, hence each user allocates its whole traffic to one of the network resources. We analyze topologies of parallel resources within a game-theoretic framework and establish several fundamental properties. We prove the existence of and convergence to a Nash equilibrium. For a broad class of residual capacity performance functions, an upper bound on the number of iterations till convergence is derived. An algorithm is presented for testing the uniqueness of the equilibrium. Sufficient conditions for achieving a feasible equilibrium are obtained. We consider extensions to general network topologies. In particular, we show that, for a class of throughput-oriented cost functions, existence of and convergence to a Nash equilibrium is guaranteed in all topologies. With these structural results at hand, we establish the foundations of a design and management methodology, that enables to operate such networks efficiently, in spite of the lack of cooperation among users and the restrictions imposed by atomic resource sharing. In particular, we study various problems pertaining to capacity allocation, pricing, and admission control, and show that their solutions are substantially different from the ones for traditional networks.