  We study condensation in one-dimensional transport models with a kinetic
constraint. The kinetic constraint results in clustering of immobile vehicles;
these clusters can grow to macroscopic condensates, indicating the onset of
dynamic phase separation between free flowing and arrested traffic. We
investigate analytically the conditions under which this occurs, and derive a
necessary and sufficient criterion for phase separation. This criterion is
applied to the well-known Nagel-Schreckenberg model of traffic flow to
analytically investigate the existence of dynamic condensates. We find that
true condensates occur only when acceleration out of jammed traffic happens in
a single time step, in the limit of strong overbraking. Our predictions are
further verified with simulation results on the growth of arrested clusters.
These results provide analytic understanding of dynamic arrest and dynamic
phase separation in one-dimensional traffic and transport models.
