A 2-phase traffic model based on a speed bound

TL;DR

This paper introduces a novel two-phase macroscopic traffic model incorporating vehicle-specific maximum speeds and a uniform speed limit, connecting microscopic and macroscopic traffic modeling approaches.

Contribution

It extends the classical LWR model to include variable maximum speeds and a speed bound, resulting in a new non-smooth 2x2 conservation law system with rigorous microscopic-macroscopic links.

Findings

The model exhibits two distinct traffic phases.

Comparison with existing models shows improved realism.

A formal link between microscopic and macroscopic models is established.

Abstract

We extend the classical LWR traffic model allowing different maximal speeds to different vehicles. Then, we add a uniform bound on the traffic speed. The result, presented in this paper, is a new macro- scopic model displaying 2 phases, based on a non-smooth 2x2 system of conservation laws. This model is compared with other models of the same type in the current literature, as well as with a kinetic one. Moreover, we establish a rigorous connection between a microscopic Follow-The-Leader model based on ordinary differential equations and this macroscopic continuum model.