A primal-dual approach to delay minimizing user association in cellular networks

We study network utility maximization (NUM) within the context of cellular single user association (SUA) policies that map each mobile user (MU) to a single base station (BS) and make use of the generalized α-proportional fairness utility measure across downlink rates. Finding an exact solution to many such centralized user association problem is known to be NP-hard, so we are motivated to consider the integer relaxation of the SUA NUM problem. On this front, we provide separate characterizations of i) the fairness measures under which the SUA NUM problem integrality gap is exactly 1, and ii) the fairness measures yielding non-convex SUA NUM problem formulations. Next, we analyze the fairness measure corresponding to delay minimization and find a more natural linearization of the non-convex minimum delay SUA problem compared to our related previous work. We propose and construct a primal-dual algorithm to approximate the linearized minimum delay SUA problem. Our primal-dual algorithm is shown to achieve smaller performance gaps and runtimes over i) an intuitive baseline rounding algorithm applied to the linearized min delay SUA problem, as well as ii) two greedy heuristics that emphasize associations with minimal MU-BS distances and maximal downlink SINR ratios, respectively.