  We consider network utility maximization problems over heterogeneous cellular
networks (HetNets) that permit dual connectivity. Dual connectivity (DC) is a
feature that targets emerging practical HetNet deployments that will comprise
of non-ideal (higher latency) connections between transmission nodes, and has
been recently introduced to the LTE-Advanced standard. DC allows for a user to
be simultaneously served by a macro node as well as one other (typically micro
or pico) node and requires relatively coarser level coordination among serving
nodes. For such a DC enabled HetNet we comprehensively analyze the problem of
determining an optimal user association, where in any feasible association each
user can be associated with (i.e., configured to receive data from) any one
macro node (in a given set of macro nodes) and any one pico node that lies in
the chosen macro node's coverage area. We consider the weighted sum rate system
utility subject to per-user maximum and minimum rate constraints, as well as
the proportional fairness (PF) system utility. For both utility choices we
construct approximation algorithms and establish their respective approximation
guarantees. We then validate the performance of our algorithms via numerical
results.
