Distribution of time-headways in a particle-hopping model of vehicular traffic

Some prototype models of interacting particles driven far from equilibrium are known to capture many qualitative features of vehicular traffic. The time headway is defined as the time interval between two successive vehicles recorded by a detector placed at a fixed position on the highway. We report analytical calculation of the distributions of the time headways in some special cases of the Nagel-Schreckenberg model, which is a particle-hopping model of vehicular traffic on idealized single-lane highways. We also present numerical results for the time-headway distribution in more general situations in this model.