Multi-Layer Decomposition of Network Utility Maximization Problems

We describe a distributed framework for resource sharing problems that arise in communications, micro-economics, and various networking applications. In particular, we consider a hierarchical multi-layer decomposition for network utility maximization (ML-NUM), where functionalities are assigned to different layers. The proposed methodology creates solutions with central management and distributed computations to the resource allocation problems. In non-stationary environments, the technique aims to respond quickly to the dynamics of the network by decreasing delay by partially shifting the communication and computational burden to the network edges. Our main contribution is a detailed analysis under the assumption that the network changes are on the same time-scale as the convergence time of the algorithms used for local computations. Moreover, assuming strong concavity and smoothness of the users' objective functions, and under some stability conditions for each layer, we present convergence rates and optimality bounds for the ML-NUM framework. In addition, the main benefits of the proposed method are demonstrated with numerical examples.