  We study fundamental characteristics for the connectivity of multi-hop D2D
networks. Devices are randomly distributed on street systems and are able to
communicate with each other whenever their separation is smaller than some
connectivity threshold. We model the street systems as Poisson-Voronoi or
Poisson-Delaunay tessellations with varying street lengths. We interpret the
existence of adequate D2D connectivity as percolation of the underlying random
graph. We derive and compare approximations for the critical device-intensity
for percolation, the percolation probability and the graph distance. Our
results show that for urban areas, the Poisson Boolean Model gives a very good
approximation, while for rural areas, the percolation probability stays far
from 1 even far above the percolation threshold.
