Phase Transition of Traffic Overloading Failures in Large Wireless Networks

Traffic overloading failures are infectious due to the correlations in their occurrence. When a node fails at excessive load, the re-routed traffic may fail other nodes in the network. We present in this paper a mathematical characterization of the resilience of large wireless networks to the traffic overloading failures. We show that as the number of failed nodes increases, the network transits from a failure-resistant phase to a failure-prone phase at certain time. We derive an upper bound on this phase transition time to provide an estimation of the maximum network resilience to traffic overloading failures.