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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