On the delay optimal user association in heterogeneous wireless networks

We consider the problem of delay minimization over the downlink of a heterogeneous wireless network (HetNet) by optimizing the association of users to transmission points (TPs) subject to per-user maximum rate constraints. The user association problem is formulated as a constrained set function minimization problem and our key result is to show that the set function is a supermodular set function. We derive alternate set functions that are also supermodular and upper bound the original one, while being simpler to optimize. We use a simple combinatorial algorithm to approximately solve the user association problem and comprehensively analyze its performance.