  The spatio-temporal organizations of vehicular traffic in cellular-automata
models with "slow-to-start" rules are qualitatively different from those in the
Nagel-Schreckenberg (NaSch) model of highway traffic. Here we study the effects
of such a slow-to-start rule, introduced by Benjamin, Johnson and Hui (BJH), on
the the distributions of the distance-headways, time-headways, jam sizes and
sizes of the gaps between successive jams by a combination of approximate
analytical calculations and extensive computer simulations. We compare these
results for the BJH model with the corresponding results for the NaSch model
and interpret the qualitative differences in the nature of the spatio-temporal
organizations of traffic in these two models in terms of a phase separation of
the traffic caused by the slow-to-start rule in the BJH model.
