  In this article we setup a dynamic device-to-device communication system
where devices, given as a Poisson point process, move in an environment, given
by a street system of random planar-tessellation type, via a random-waypoint
model. Every device independently picks a target location on the street system
using a general waypoint kernel, and travels to the target along the shortest
path on the streets with an individual velocity. Then, any pair of devices
becomes connected whenever they are on the same street in sufficiently close
proximity, for a sufficiently long time. After presenting some general
properties of the multi-parameter system, we focus on an analysis of the
clustering behavior of the random connectivity graph. In our main results we
isolate regimes for the almost-sure absence of percolation if, for example, the
device intensity is too small, or the connectivity time is too large. On the
other hand, we exhibit parameter regimes of sufficiently large intensities of
devices, under favorable choices of the other parameters, such that percolation
is possible with positive probability. Most interestingly, we also show an
in-and-out of percolation as the velocity increases. The rigorous analysis of
the system mainly rests on comparison arguments with simplified models via
spatial coarse graining and thinning approaches. Here we also make contact to
geostatistical percolation models with infinite-range dependencies.
