On the fundamental diagram of traffic flow

TL;DR

This paper introduces a generalized fluid-dynamical traffic flow model that incorporates experimental data-driven source terms, capturing the unstable regimes and reproducing the inverse-$$ shape of the fundamental diagram.

Contribution

It extends existing models by including more general source terms based on experimental data, capturing unstable traffic regimes.

Findings

The new model exhibits linearly unstable regimes consistent with traffic dynamics.

Numerical simulations reproduce the inverse-$$ shape of the fundamental diagram.

The model aligns with observed traffic flow behaviors.

Abstract

We present a new fluid-dynamical model of traffic flow. This model generalizes the model of Aw and Rascle [SIAM J. Appl. Math. 60 916-938] and Greenberg [SIAM J. Appl. Math 62 729-745] by prescribing a more general source term to the velocity equation. This source term can be physically motivated by experimental data, when taking into account relaxation and reaction time. In particular, the new model has a (linearly) unstable regime as observed in traffic dynamics. We develop a numerical code, which solves the corresponding system of balance laws. Applying our code to a wide variety of initial data, we find the observed inverse-$\lambda$ shape of the fundamental diagram of traffic flow.