Stationary Velocity Distributions in Traffic Flows

Abstract

We introduce a traffic flow model that incorporates clustering and passing. We obtain analytically the steady state characteristics of the flow from a Boltzmann-like equation. A single dimensionless parameter, R=c_0v_0t_0 with c_0 the concentration, v_0 the velocity range, and 1/t_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^α form, and the flux is J ~ R^{-γ}. The initial distribution of slow cars governs the statistics. When P_0(v) ~ v^μ 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.

7 pages, 3 figures, revtex

References in corpus (2)

• Gas-kinetic derivation of Navier-Stokes-like traffic equations
• Exact Steady States of Disordered Hopping Particle Models with Parallel and Ordered Sequential Dynamics

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