Stationary Velocity Distributions in Traffic Flows,

E. Ben-Naim and P.L. Krapivsky

The role of the passing mechanism in traffic flows is examined. From a Boltzmann equation approach, steady state properties of the flow such as the flux, the average cluster size, and the velocity distributions are found analytically. 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 behavior. Furthermore, the velocity distributions may exhibit a ``triple deck'' boundary layer structure.


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