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

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 has not 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 usual stochastic macroscopic models.