Diffusion in single-lane freeway traffic

Abstract

Superdiffusion is normally observed in random walks that are subjected to a directed force: the mean-square displacement is proportional to t^α with scaling exponent α ≥ 2. Ideally, vehicular traffic should show the same behavior. Through simulated highway traffic, we demonstrate that car density and driving fluctuations alter the overall behavior of cars during both transient and steady states. We further show that driving fluctuation can scale the motion down to a subdiffusive state (α < 1) that persists over a long period. Finally, we discuss the crossover time from transient to steady state.