Connectivity and critical point behavior in mobile ad hoc and sensor networks

A well-known approach to increase the resilience of mobile ad hoc networks (MANETs) and unstructured sensor networks is to ensure a network topology where there are at least k disjoint routes in the network between each pair of network nodes (usually called k-connectivity). Asymptotic analyses of node density requirements for k-connectivity have been considered in the literature. In this paper, we present the results of a simulation study investigating the relationship between asymptotic results in the literature and k-connectivity under varying nodal density and nodal degree. The numerical results illustrate where the asymptotic approximations breakdown and we show that this largely due to the existence of critical connectivity points in the topology. Using a critical point identification algorithm we examine how the number of critical points varies with nodal degree, nodal density and node mobility. In addition, critical point is evaluated its effectiveness on the network caused by failure.