  We study downlink delay minimization within the context of cellular user
association policies that map mobile users to base stations. We note the delay
minimum user association problem fits within a broader class of network utility
maximization and can be posed as a non-convex quadratic program. This
non-convexity motivates a split quadratic objective function that captures the
original problem's inherent tradeoff: association with a station that provides
the highest signal-to-interference-plus-noise ratio (SINR) vs. a station that
is least congested. We find the split-term formulation is amenable to
linearization by embedding the base stations in a hierarchically well-separated
tree (HST), which offers a linear approximation with constant distortion. We
provide a numerical comparison of several problem formulations and find that
with appropriate optimization parameter selection, the quadratic reformulation
produces association policies with sum delays that are close to that of the
original network utility maximization. We also comment on the more difficult
problem when idle base stations (those without associated users) are
deactivated.
