Overload Network Failures: An Approach from the Random-Walk Model

We investigate analytically the robustness of scale-free networks against overload failures in percolation and cascading processes. Modeling fluctuating loads in a network by random walkers, it is found that there exist two kinds of robustness of networks against overload failures in the percolation process. One is measured by the critical total load W_rmc and the other is by the critical node removal fraction f_rmc. Enhancing the scale-free property, networks become fragile in both senses. In contrast, the increase of the node tolerance parameter makes scale-free networks robust in the sense of W_rmc but fragile in the sense of f_rmc. In addition, we treat the cascading overload process by considering it as a chain of percolation processes. We show that scale-free networks are robust against cascading overload failures modeled by random walkers, which is opposed to most of the previous results.