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