A class of multi-phase traffic theories for microscopic, kinetic and continuum traffic models

TL;DR

This paper reviews and compares multi-phase traffic theories across microscopic, kinetic, and continuum models, highlighting their similarities, differences, and the conditions under which phase transitions and stop-and-go waves occur.

Contribution

It introduces a unified review and numerical comparison of multi-phase traffic models derived from microscopic, kinetic, and macroscopic perspectives.

Findings

Models show similar behavior in stop-and-go wave formation

Phase transitions occur near bottlenecks depending on local density

Most models exhibit multi-valued fundamental diagrams

Abstract

In the present paper a review and numerical comparison of a special class of multi-phase traffic theories based on microscopic, kinetic and macroscopic traffic models is given. Macroscopic traffic equations with multi-valued fundamental diagrams are derived from different microscopic and kinetic models. Numerical experiments show similarities and differences of the models, in particular, for the appearance and structure of stop and go waves for highway traffic in dense situations. For all models, but one, phase transitions can appear near bottlenecks depending on the local density and velocity of the flow.