Percolation Processes and Wireless Network Resilience to Degree-Dependent and Cascading Node Failures

We study the problem of wireless network resilience to node failures from a percolation-based perspective. In practical wireless networks, it is often the case that the failure probability of a node depends on its degree (number of neighbors). We model this phenomenon as a degree-dependent site percolation process on random geometric graphs. Due to its non-Poisson structure, degree-dependent site percolation is far from a trivial generalization of independent site percolation. Using coupling and renormalization method, we obtain analytical conditions for the existence of phase transitions within the degree-dependent failure model. Furthermore, in networks carrying traffic load, the failure of one node can result in redistribution of the load onto other nearby nodes. If these nodes fail due to excessive load, then this process can result in a cascading failure. Using a simple but descriptive model, we show that the cascading failure problem for large-scale wireless networks is equivalent to a degree-dependent site percolation on random geometric graphs. We obtain analytical conditions for cascades in this model. To our knowledge, this work represents the first investigation of cascading phenomena in networks with geometric constraints.