Network connectivity with heterogeneous mobility

We study the issue of mobile wireless network (MWN) connectivity. In particular, we investigate the smallest communication or transmission range of the nodes necessary for connectivity of MWNs, which we call the critical transmission range (CTR). Unlike many of existing studies, however, the mobilities of the nodes are not assumed homogeneous, and the locations of the nodes are not identically distributed. We examine the distribution of CTR when the number of nodes in the network is large. We show that, under some conditions, the CTR is inversely proportional to the infimum of the average spatial density of the nodes in the network and its distribution goes through a phase transition over a small range.