Resilience to Degree-Dependent and Cascading Node Failures in Random Geometric Networks

This paper studies the problem of resilience to node failures in large-scale networks modelled by random geometric graphs. Adopting a percolation-based viewpoint, the paper investigates the ability of the network to maintain global communication in the face of dependent node failures. Degree-dependent site percolation processes on random geometric graphs are examined, and the first known analytical conditions are obtained for the existence and non-existence, respectively, of a large connected component of operational network nodes after degree-dependent node failures. In electrical power networks or wireless communication and computing networks, cascading failure from power blackouts or virus epidemics may result from a small number of initial node failures triggering global failure events affecting the whole network. With the use of a simple but descriptive model, it is shown that the cascading failure problem is equivalent to a degree-dependent percolation process. The first analytical conditions are obtained for the occurrence and non-occurrence of cascading failures, respectively, in large-scale networks with geometric constraints.