Stationary Velocity Distributions in Traffic Flows

the steady state characteristics of the flow from a Boltzmann-like equation. A single dimensionless parameter, R = c0v0t0 with c0 the concentration, v0 the velocity range, and t −1 0 the passing rate, determines the nature of the steady state. When R 1, uninterrupted flow with single cars occurs. When R 1, large clusters with average mass 〈m〉 ∼ R form, and the flux is J ∼ R−γ . The initial distribution of slow cars governs the statistics. When P0(v) ∼ v as v → 0, the scaling exponents are γ = 1/(μ+ 2), α = 1/2 when μ > 0, and α = (μ+ 1)/(μ+ 2) when μ < 0.