Network utility maximisation framework with multiclass traffic

The concave utilities in the basic network utility maximisation (NUM) problem are only suitable for elastic flows. In networks with both elastic and inelastic traffic, the utilities of inelastic traffic are usually modelled by the sigmoidal functions which are non-concave functions. Hence, the basic NUM problem becomes a non-convex optimisation problem. To address the non-convex NUM, the authors approximate the problem which is equivalent to the original one to a strictly convex problem. The approximation problem is solved efficiently via its dual by the gradient algorithm. After a series of approximations, the sequence of solutions to the approximation problems converges to a local optimal solution satisfying the Karush-Kuhn-Tucker conditions of the original problem. The proposed algorithm converges with any value of link capacity. The authors also extend their work to jointly allocate the rate and the power in a multihop wireless network with elastic and inelastic traffic. Their framework can be used for any log-concave utilities.