Dynamical phases and hysteresis in a simple one-lane traffic model

TL;DR

This paper introduces a simple two-parameter traffic model that captures complex phenomena like phase transitions, hysteresis, and jam formation, closely mirroring real traffic behavior.

Contribution

The study presents a minimalistic car-following model demonstrating rich dynamical phenomena, including phase transitions and hysteresis, with potential for calibration to real traffic data.

Findings

Traffic jams can spontaneously form in the model.

Hysteresis observed in the flux-density relationship.

Coexistence of different traffic regimes and wave propagation.

Abstract

A two parameter model for single lane car-following is introduced and its equilibrium and non-equilibrium properties are studied. Despite its simplicity, this model exhibits a rich phenomenology, analogous to that observed in real traffic, like transitions between different dynamical regimes and hysteresis in the fundamental flux-density diagram. We show that traffic jams can spontaneously appear in clustered-like structures. In the jammed phase, we observe a slow relaxation phenomenon ruled by the outgoing car flux that determines the hysteretic dependence of the fundamental flux-density diagram. Coexisting phase regimes are also evidenced so as propagating or stationary density waves. The model can be easily calibrated to reproduce experimental observations.