Random Node Failures and Wireless Networks Connectivity: Theoretical Analysis

Abstract

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.