Random Node Failures and Wireless Networks Connectivity: Theoretical Analysis

Multi-radio multi-channel wireless networks (M ²WNs) have been studied intensively over the past decade with focusing on traffic management functionalities such as channel-to-interface assignment, traffic routing and scheduling. These developed solutions always assumed continuous normal operation of all network components while failing to take into considering the failure-prone nature of wireless networks. This article analyzes the effects of node failure on the ability of network nodes to maintain their connectivity. More precisely, we present a tight upper bound on the node failure probabilities needed to maintain full network connectivity on the one hand. On the other hand, a lower bound, at which the system loses connectivity, is also derived. We show that these bounds are dependent only on the nodes´ geometric distribution and density. We then verify these theoretical results against those obtained via experimentation.