Monotonic optimization method for general utility maximization in random-access networks

Random medium access control (MAC) is extensively used in wireless communication systems as a means to allocate the shared radio resource in a distributed manner. However, some of the ultimate performance limits, including the maximum throughput, are not well understood due to the non-convex nature of the utility optimization problem. In this paper, we introduce the monotonic optimization method to tackle the intractability of nonconvex utility maximization problems in random-access networks. We show that the optimal random MAC problem can be transformed to a canonical monotonic optimization and thus can be efficiently solved using the polyblock outer approximation algorithm. We also show that the conventional polyblock outer approximation algorithm can be significantly simplified by exploiting the unique problem structure of the optimal random MAC. Based on the proposed method, we perform extensive evaluations of the optimal performance in both fully interfered and partially interfered networks. Our results here would help to understand the fundamental limits of random-access networks, and spur the study on the practical random MAC protocols to find the optimal parameters that maximize a system utility.