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.