  In order to develop a toy model for car's traffic in cities, in this paper we
analyze, by means of numerical simulations, the transition among fluid regimes
and a congested jammed phase of the flow of "kinetically constrained" hard
spheres in planar random networks similar to urban roads. In order to explore
as timescales as possible, at a microscopic level we implement an event driven
dynamics as the infinite time limit of a class of already existing model (e.g.
"Follow the Leader") on an Erdos-Renyi two dimensional graph, the crossroads
being accounted by standard Kirchoff density conservations. We define a
dynamical order parameter as the ratio among the moving spheres versus the
total number and by varying two control parameters (density of the spheres and
coordination number of the network) we study the phase transition. At a
mesoscopic level it respects an, again suitable adapted, version of the
Lighthill-Whitham model, which belongs to the fluid-dynamical approach to the
problem. At a macroscopic level the model seems to display a continuous
transition from a fluid phase to a jammed phase when varying the density of the
spheres (the amount of cars in a city-like scenario) and a discontinuous jump
when varying the connectivity of the underlying network.
