1998/08/14 by E. Ben-Naim, E. Ben‐Naim, P. L. Krapivsky · 2 citations
Engineering · Physics and Astronomy · Social Sciences · #Traffic Prediction and Management Techniques #Traffic control and management #Transportation Planning and Optimization #comp-gas #cond-mat.stat-mech #nlin.CG
paper · pdf · doi:10.1103/physreve.59.88
published as Phys. Rev. E 59, 88 (1999) · revtex, 10 pages
arxiv created 1998/08/14 · openalex publication_date 1999/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate traffic flows using the kinetic Boltzmann equations with a Maxwell collision integral. This approach allows analytical determination of the transient behavior and the size distributions. The relaxation of the car and cluster velocity distributions towards steady state is characterized by a wide range of velocity- dependent relaxation scales, R1/2<\ensuremathτ(v)<R, with R the ratio of the passing and the collision rates. Furthermore, these relaxation time scales decrease with the velocity, with the smallest scale corresponding to the decay of the overall density. The steady-state cluster size distribution follows an unusual scaling form Pm\ensuremath∼〈m〉^\ensuremath-4\ensuremathΨ(m/〈m〉2). This distribution is primarily algebraic, Pm\ensuremath∼m^\ensuremath-3/2, for m\ensuremath≪〈m〉2, and is exponential otherwise.