Connectivity Analysis of Clustered Ad Hoc and Mesh Networks

We investigate the impact of network topology on connectivity of wireless mesh and ad hoc networks. In particular we study the transmission range required to establish connectivity with some fixed proportion of network nodes. Our analysis shows that in practice it can be useful to relax the requirement of a full 100 % connectivity in ad hoc networks. We show that high network connectivity can be reached with much lower power consumption and careful node distribution strategies compared to establishment of full connectivity. Unlike most previous works we focus on non-uniform distributions of nodes. We introduce and apply modified Thomas point processes and power-law based Stoyan model for generating the locations of nodes. We show also that simple one-dimensional studies, although important, should be extended also to higher dimensional cases in order to achieve reliable results for practical network optimization purposes. Furthermore, we introduce a link between spatial correlations and the number of neighbours. This information can be used in practical topology estimation. Finally, we comment on the realism of our topology claims.