Percolation processes and wireless network resilience

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 nodes with larger degrees (i.e., more neighbors) are more likely to fail. We model this phenomenon as a degree-dependent site percolation process on random geometric graphs. In particular, we obtain analytical conditions for the existence of phase transitions within this 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 cascading failure. We analyze this cascading failures problem in large-scale wireless networks, and show that it is equivalent to a degree-dependent site percolation on random geometric graphs. We obtain analytical conditions for cascades in this model.