A mesoscopic approach on stability and phase transition between different traffic flow states

TL;DR

This paper presents a mesoscopic physics-inspired model to analyze traffic flow stability and phase transitions, successfully reproducing key features of real traffic data and explaining oscillations and congestion phenomena.

Contribution

It introduces a novel mesoscopic approach linking phase transition theory to traffic flow dynamics, extending to higher dimensions and explaining observed oscillations.

Findings

Model reproduces the inverse-$\\lambda$ shape of the fundamental diagram.

Captures wide scattering of congested traffic data.

Explains temporal oscillations as curl of a vector field.

Abstract

It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong resemblance to the phase transition in thermodynamics. In this work, we explore the underlying physics of the traffic system, by examining closely the physical properties and mathematical constraints of the phase transitions therein. By using a mesoscopic approach, one entitles the catastrophe model the same physical content as in the Landau's theory, and uncovers its close connections to the instability of the equation of motion and to the transition between different traffic states. In addition to the one-dimensional configuration space, we generalize our discussions to the higher-dimensional case, where the observed temporal oscillation in traffic flow data is attributed to the curl of a vector field. We exhibit that our model can reproduce the main features of the observed fundamental diagram including the inverse-$\lambda$ shape and the wide scattering of congested traffic data. When properly parameterized, the main feature of the data can be reproduced reasonably well either in terms of the oscillating congested traffic or in terms of the synchronized flow.