Steady-state properties of traffic flows

The role of the passing mechanism in traffic flows is examined. Specifically, we consider passing rates that are proportional to the difference between the velocities of the passing car and the passed car. From a Boltzmann equation approach, steady-state properties of the flow such as the flux, average cluster size, and velocity distributions are found analytically. We show that a single dimensionless parameter determines the nature of the flow and helps distinguish between dilute and dense flows. For dilute flows, perturbation expressions are obtained, while for dense flows a boundary layer analysis is carried out. In the latter case, extremal properties of the initial velocity distribution underly the leading scaling asymptotic behaviour. For dense flows, the stationary velocity distribution exhibits a rich ‘triple-deck ’ boundary layer structure. Furthermore, in this regime fluctuations in the flux may become extremely large.