  The performance of different combinations of user association (UA) and
resource allocation (RA) in heterogeneous cellular networks has been
extensively studied using a classic modeling approach based on system
snapshots. There have been also many studies focusing on the dynamics of the
system using queueing models. These modeling approaches are rarely compared
with each other though they each bring different insights to the design
problem. In this paper, we consider a queueing model-based approach to study
the interplay of UA and RA, and compare the results to those obtained using
snapshot models. Specifically, we formulate three different joint UA and RA
optimization problems corresponding to the following three performance metrics:
the maximum achievable arrival rate, the average system delay, and the maximum
per-user delay. These problems are non-convex integer programs. We have
therefore developed numerical techniques to compute either their exact
solutions or tight lower bounds. We obtain results for different combinations
of RA and UA schemes, and compare the trends with those obtained via the
snapshot approach. The trends on RA are very similar, which we take as a
cross-validation of the two modeling approaches for this kind of problem. The
trends on user association are somewhat different which indicates a lack of
robustness of the results and the need for a careful validation of UA models.
