Estimation of the Percolation Threshold for D2D Networks on Urban Road Models

Multi-hop device-to-device (D2D) has been considered as a key technology for future wireless communication networks in 5G. We studied this type of D2D networks using a stochastic geometry model to represent the devices communications on urban areas. We modelled the urban street system as a Poisson-Voronoi tessellation (PVT) and devices were randomly distributed following a one-dimensional Poisson point process on each edge of the tessellation. Setting the distance of communication that can be reached, we consider the corresponding Gilbert graph. We considered that a large number of devices are connected over large distances on the territory if there exists an infinite connected component of the graph. In this paper, we compare several different methods for the estimation of the percolation threshold of the graph. We show that the best estimations with the smallest variance are obtained through a torus model. We also show that in the case of dense urban area, the percolation threshold is close to the Poisson Boolean model's one.