Non-convex resource allocation in communication networks

The continuously growing number of applications competing for resources in current communication networks highlights the necessity for efficient resource allocation mechanisms to maximize user satisfaction. Optimization Theory can provide the necessary tools to develop such mechanisms that will allocate network resources optimally and fairly among users. However, the resource allocation problem in current networks has characteristics that turn the respective optimization problem into a non-convex one. First, current networks very often consist of a number of wireless links, whose capacity is not constant but follows Shannon capacity formula, which is a non-convex function. Second, the majority of the traffic in current networks is generated by multimedia applications, which are non-concave functions of rate. Third, current resource allocation methods follow the (bandwidth) proportional fairness policy, which when applied to networks shared by both concave and non-concave utilities leads to unfair resource allocations. These characteristics make current convex optimization frameworks inefficient in several aspects. This work aims to develop a non-convex optimization framework that will be able to allocate resources efficiently for non-convex resource allocation formulations. Towards this goal, a necessary and sufficient condition for the convergence of any primal-dual optimization algorithm to the optimal solution is proven. The wide applicability of this condition makes this a fundamental contribution for Optimization Theory in general. A number of optimization formulations are proposed, cases where this condition is not met are analysed and efficient alternative heuristics are provided to handle these cases. Furthermore, a novel multi-sigmoidal utility shape is proposed to model user satisfaction for multi-tiered multimedia applications more accurately. The advantages of such non-convex utilities and their effect in the optimization process are thoroughly examined. Alternative allocation policies are also investigated with respect to their ability to allocate resources fairly and deal with the non-convexity of the resource allocation problem. Specifically, the advantages of using Utility Proportional Fairness as an allocation policy are examined with respect to the development of distributed algorithms, their convergence to the optimal solution and their ability to adapt to the Quality of Service requirements of each application