  The strength and stability properties of hierarchical load bearing networks
and their strengthened variants have been discussed in recent work. Here, we
study the avalanche time distributions on these load bearing networks. The
avalanche time distributions of the V- lattice, a unique realization of the
networks, show power-law behavior when tested with certain fractions of its
trunk weights. All other avalanche distributions show Gaussian peaked behavior.
Thus the V- lattice is the critical case of the network. We discuss the
implications of this result.
