Impact of the Dynamic Membership in the Connectivity Graph of the Wireless Ad hoc Networks

Mobility Metrics of the connectivity graphs with fixed number of nodes have been presented in several research studies over the last three years. More realistic mobility models that are derived from real user traces challenge the assumption of the connectivity graph with fixed number of nodes, but they rather show that wireless nodes posses dynamic membership (nodes join and leave the simulation dynamically based on some random variable). In this paper, we evaluate the mobility metrics of the dynamic connectivity graph on both the nodes and the links. The contributions of this paper are two-fold. First, we introduce the algorithm that computes the Maximum Node Degree. We show that the Maximum Node Degree, which characterizes the dynamic membership property, impacts the connectivity mobility metrics of the Link and Path Durations of the dynamic connectivity graphs. Second, we provide the lower and the upper bounds for these mobility metrics.