  We study the Biroli-Mezard model for lattice glasses on a number of
hierarchical networks. These networks combine certain lattice-like features
with a recursive structure that makes them suitable for exact renormalization
group studies and provide an alternative to the mean-field approach. In our
numerical simulations here, we first explore their equilibrium properties with
the Wang-Landau algorithm. Then, we investigate their dynamical behavior using
a grand-canonical annealing algorithm. We find that the dynamics readily falls
out of equilibrium and jams in many of our networks with certain constraints on
the neighborhood occupation imposed by the Biroli-Mezard model, even in cases
where exact results indicate that no ideal glass transition exists. But while
we find that time-scales for the jams diverge, our simulations cannot ascertain
such a divergence for a packing fraction distinctly above random close packing.
In cases where we allow hopping in our dynamical simulations, the jams on these
networks generally disappear.
