Critical Phase of Connectivity in Wireless Network Expansion

In this paper, we study the transition phase in the network connectivity. We focus on the critical time points that mark the network transformation from partition to connected state following a growth of node density. The percolation theory is used to analyze the relationship between the density increase process and the connectivity transition. Specifically, we derive the lower bound and the upper bound of critical density points against node transmission range. We also use three growth functions of node density to obtain the first connection time and the total connection time which denote the critical points when the node densities reach the lower bound and upper bound of critical value respectively. The simulation demonstrates the evolution of network in terms of the connectivity and gives the connection times with three different growth models.