Optimal bandwidth control subject to the user-grouping constraint

We study the bandwidth allocation problem in the paper. Unlike the conventional models on many similar problems, our model focuses on the constrained bandwidth availability of users. Specifically, suppose the bandwidth allocation to each user has lower and upper bounds and the total bandwidth allocation to some group of users has lower and upper bounds as well. Under this setting we give a game-theoretic analysis on the optimal bandwidth control. In particular, under mild assumptions on the utility function of each user we prove the the existence, uniqueness and fairness, in some appropriate sense, of the Nash equilibrium point in the allocation game. Also, an algorithm that identifies the equilibrium point is proposed and illustrated with a numerical example.