  A new class of probabilistic models for cascading failure propagation in
interconnected systems is proposed. The models take into account important
characteristics of real systems that are not considered in existing generic
approaches. Specifically, it is assumed that the load increments after a
failure are proportional to the failed load and that the load redistribution
among the remaining elements is stochastic. The models are solved analytically
in terms of generalized branching processes, and the failure propagation
properties of a prototype example are analyzed in detail.
