Macroscopic Manifestations of Traffic Waves in Microscopic Models

TL;DR

This paper investigates how microscopic car-following models produce macroscopic traffic waves, providing a systematic framework to connect individual vehicle dynamics with observable traffic flow patterns and fundamental diagrams.

Contribution

It introduces a hierarchical testing approach linking microscopic models to macroscopic traffic phenomena, enhancing understanding of traffic wave formation and shape of fundamental diagrams.

Findings

Macroscopic flow quantities can be derived from microscopic models in unstable regimes.

Traffic wave structures influence the shape of fundamental diagrams.

The framework applies to common microscopic models, aiding traffic flow analysis.

Abstract

Traffic waves can rise even from single lane car-following behaviour. To better understand and mitigate traffic waves, it is necessary to use analytical tools like mathematical models, data analysis, and micro-simulations that can capture the dynamics of real traffic flow. In this study, we isolate car-following dynamics and present a systematic hierarchy of tests that connect the microscopic scale with the meaningful macroscopic effective state in the presence of waves. This allows insights with precise attributable cause-to-effect relationships of specific observed traffic patterns. We establish a principled way of generating macroscopic flow quantities from microscopic models in the unstable regime. Those quantities are then used to study how the corresponding non-equilibrium wave structures manifest in the fundamental diagram, based on three basic scenarios that can serve as building blocks for understanding more complex micro-simulation studies. Finally, this study gives insight on the shapes of the reduced fundamental diagrams for different commonly used microscopic models.