  Robustness of routing policies for networks is a central problem which is
gaining increased attention with a growing awareness to safeguard critical
infrastructure networks against natural and man-induced disruptions. Routing
under limited information and the possibility of cascades through the network
adds serious challenges to this problem. This abstract considers the framework
of dynamical networks introduced in our earlier work [1,2], where the network
is modeled by a system of ordinary differential equations derived from mass
conservation laws on directed acyclic graphs with a single origin-destination
pair and a constant inflow at the origin. The rate of change of the particle
density on each link of the network equals the difference between the inflow
and the outflow on that link. The latter is modeled to depend on the current
particle density on that link through a flow function. The novel modeling
element in this paper is that every link is assumed to have finite capacity for
particle density and that the flow function is modeled to be strictly
increasing as density increases from zero up to the maximum density capacity,
and is discontinuous at the maximum density capacity, with the flow function
value being zero at that point. This feature, in particular, allows for the
possibility of spill-backs in our model. In this paper, we present our results
on resilience of such networks under distributed routing, towards perturbations
that reduce link-wise flow functions.
