High-fidelity macroscopic traffic equations

Abstract

The Euler-like traffic equations that can be derived for quasi-homogeneous traffic situations are corrected for non-equilibrium effects. This yields additional transport terms describing a flux of velocity variance. Other modifications resulting in a bulk viscosity term arise from the adaptive behavior of drivers with respect to changes of the traffic situation. Finally, corrections due to the space requirements of vehicles as well as due to finite reaction- and braking-times are introduced. These are responsible for a van der Waals-like relation for ‘traffic pressure’ and modified relations for the kinetic coefficients.