Modeling highway-traffic headway distributions using superstatistics

We study traffic clearance distributions (i.e., the instantaneous gap between successive vehicles) and time-headway distributions by applying the Beck and Cohen superstatistics. We model the transition from free phase to congested phase with the increase of vehicle density as a transition from the Poisson statistics to that of the random-matrix theory. We derive an analytic expression for the spacing distributions that interpolates from the Poisson distribution and Wigner's surmise and apply it to the distributions of the net distance and time gaps among the succeeding cars at different densities of traffic flow. The obtained distribution fits the experimental results for single-vehicle data of the Dutch freeway A9 and the German freeway A5.