PARTICLE-HOPPING MODELS OF VEHICULAR TRAFFIC - DISTRIBUTIONS OF DISTANCE HEADWAYS AND DISTANCE BETWEEN JAMS

We calculate the distribution of the distance headways (i.e., the inst antaneous gap between successive vehicles) as well as the distribution of instantaneous distance between successive jams in the Nagel-Schrec kenberg (NS) model of vehicular traffic. When the maximum allowed spee d, V-max, of the vehicles is larger than unity, over an intermediate r ange of densities of vehicles, our Monte Carlo (MC) data for the dista nce headway distribution exhibit two peaks, which indicate the coexist ence of ''free-flowing'' traffic and traffic jams. Our analytical argu ments clearly rule out the possibility of occurrence of more than one peak in the distribution of distance headways in the NS model when V-m ax = 1 as well as in the asymmetric simple exclusion process. Modifyin g and extending an earlier analytical approach for the NS model with V -max = 1, and introducing a novel transfer matrix technique, we also c alculate the exact analytical expression for the distribution of dista nce between the jams in this model; the corresponding distributions fo r V-max > 1 have been computed numerically through MC simulation.