The random access NUM with multiclass traffic

In this article, we consider the network utility maximization (NUM) problem for the random access network with multiclass traffic. The utilities associated with the users are not only concave, but also nonconcave functions. Consequently, the random access NUM problem becomes more difficult to solve. Based on the successive approximation method, we propose an algorithm that jointly controls the rate and the persistent probability of the users. The proposed algorithm converges to a suboptimal solution to the original problem which also satisfies the Karush–Kuhn–Tucker conditions. We also generalize the framework so that a broader choice of utility functions can be applied.