Network Connectivity with a Family of Group Mobility Models

We investigate the communication range of the nodes necessary for network connectivity, which we call bidirectional connectivity, in a simple setting. Unlike in most of existing studies, however, the locations or mobilities of the nodes may be correlated through group mobility: nodes are broken into groups, with each group comprising the same number of nodes, and lie on a unit circle. The locations of the nodes in the same group are not mutually independent, but are instead conditionally independent given the location of the group. We examine the distribution of the smallest communication range needed for bidirectional connectivity, called the critical transmission range (CTR), when both the number of groups and the number of nodes in a group are large. We first demonstrate that the CTR exhibits a parametric sensitivity with respect to the space each group occupies on the unit circle. Then, we offer an explanation for the observed sensitivity by identifying what is known as a very strong threshold and asymptotic bounds for CTR.