Stability analysis of stochastic second-order macroscopic continuum models and numerical simulations

TL;DR

This paper investigates how stochastic factors influence the stability of second-order macroscopic traffic flow models, revealing that stochasticity generally destabilizes traffic flow through analytical and numerical methods.

Contribution

It provides the first comprehensive stability analysis of stochastic second-order macroscopic models using the direct Lyapunov method, highlighting the destabilizing effect of stochasticity.

Findings

Stochasticity destabilizes traffic flow in the models.

Analytical stability results are validated by numerical simulations.

The proposed methodology is more efficient than existing approaches.

Abstract

Second-order macroscopic continuum models have been constantly improving for decades to reproduce the empirical observations. Recently, a series of experimental studies have suggested that the stochastic factors contribute significantly to destabilizing traffic flow. Nevertheless, the traffic flow stability of the stochastic second-order macroscopic continuum model hasn't received the attention it deserves in past studies. More importantly, we have found that the destabilizing aspect of stochasticity is still not correctly validated in the existing theoretical stability analysis. In this paper, we analytically study the impact of stochasticity on traffic flow stability for a general stochastic second-order macroscopic model by using the direct Lyapunov method. Numerical simulations have been carried out for different typical stochastic second-order macroscopic models. Our analytical stability analysis has been validated, and our methodology has been proved more efficient. Our study has theoretically revealed that the presence of stochasticity has a destabilizing effect in stochastic macroscopic models.