To study the overall connectivity in device-to-device networks in cities, we
incorporate a signal-to-interference-plus-noise connectivity model into a
Poisson-Voronoi tessellation model representing the streets of a city. Relays
are located at crossroads (or street intersections), whereas (user) devices are
scattered along streets. Between any two adjacent relays, we assume data can be
transmitted either directly between the relays or through users, given they
share a common street. Our simulation results reveal that the network
connectivity is ensured when the density of users (on the streets) exceeds a
certain critical value. But then the network connectivity disappears when the
user density exceeds a second critical value. The intuition is that for longer
streets, where direct relay-to-relay communication is not possible, users are
needed to transmit data between relays, but with too many users the
interference becomes too strong, eventually reducing the overall network
connectivity. This observation on the user density evokes previous results
based on another wireless network model, where transmitter-receivers were
scattered across the plane. This effect disappears when interference is removed
from the model, giving a variation of the classic Gilbert model and recalling
the lesson that neglecting interference in such network models can give overly
optimistic results. For physically reasonable model parameters, we show that
crowded streets (with more than six users on a typical street) lead to a sudden
drop in connectivity. We also give numerical results outlining a relationship
between the user density and the strength of any interference reduction
techniques