Maxwell Model of Traffic Flows

Details Maxwell Model of Traffic Flows Maxwell Model of Traffic Flows

1998-08-14

arxiv.org/abs/cond-mat/9808162v1

Phys. Rev. E 59, 88 (1999)

Physics

Condensed Matter

Statistical Mechanics

revtex, 10 pages

Scientific paper

10.1103/PhysRevE.59.88

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, $R^{1/2}<\tau(v)^{-4} \Psi(m/< m>^2)$. This distribution is primarily algebraic, $P_m\sim m^{-3/2}$, for $m\ll < m>^2$, and is exponential otherwise.

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