MotionCast: General Connectivity in Clustered Wireless Networks

Abstract

We propose a novel concept of \((k,m)\)-connectivity in mobile clustered wireless networks, in which there are \(n\) mobile cluster members and \(n^d\) static cluster heads. \((k,m)\)-connectivity signifies that in each time period consisting of \(m\) time slots, there exist at least \(k\) time slots, during any one of which every cluster member can directly communicate with at least one cluster head. We investigate the critical transmission range of asymptotic \((k,m)\)-connectivity when cluster members move according to random walk or i.i.d. mobility model. Under random walk model, we propose two general heterogeneous velocity models which characterize an inherent property of many applied wireless networks that cluster members move with different velocities. We define weak and strong parameters conditions under both mobility models and analyze the probability that the network is asymptotically \((k,m)\)-connected, denoted as \(P(\fancyscript{C})\). For both mobilities, under weak parameters condition, we provide bounds on \(P(\fancyscript{C})\) and derive the critical transmission range for \((k,m)\)-connectivity. For random walk mobility and i.i.d. mobility, under strong parameters condition, we present a precise asymptotic probability distribution of \(P(\fancyscript{C})\) in terms of the transmission radius. Our results provide fundamental insights and theoretical guidelines on design of large-scale wireless networks.