Maxwell model of traffic flows

We investigate traffic flows using the kinetic Boltzmann equations with a M axwell collision integral. This approach allows analytical determination of the transient behavior and the size distributions. The relaxation of the c ar and cluster velocity distributions towards steady state is characterized by a wide range of velocity-dependent relaxation scales, R-1/2< tau(upsilo n)<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 P(m)similar to[m] (-4)Psi(m/[m](2)). This distribution is primarily algebraic, P(m)similar to m(-3/2), for m much less than[m](2), and is exponential otherwise. [S1063- 651X(98)14812-2].