A novel stochastic second-order macroscopic continuum traffic flow model for traffic instability

Dispersion of vehicle speed often causes traffic instability, which affects traffic efficiency and safety. Previous studies have demonstrated that fluctuations near the steady-state equilibrium of traffic flow can be attributed to the stochasticity of traffic system leading by large vehicle speed dispersion. However, the intrinsic mechanisms between fluctuations of traffic flow and vehicle speed dispersion need further discussion. Therefore, a novel stochastic extended speed gradient model based on the fast-and-low speed vehicles is proposed to describe their relationships in this paper. Firstly, a speed-dependent stochastic process is characterized for the stochastic deviation of velocity dispersion, and a stochastic high-order macroscopic traffic flow model is constructed for fast and low speed vehicles. Secondly, using Lyapunov stability theorem and its derivatives, the linear stability criterion of the proposed model is derived. The theoretical results also indicate that the steady-state equilibrium of traffic flow is profoundly affected by the traffic flow initial density, penetration rate of fast and low speed vehicles, and noise intensity. Hence, simulations are implemented from the above three parameters. It can be found that the critical values of initial density affecting traffic flow stability are pursued, and some detailed tendencies of traffic flow are explored for different parameters. Finally, the model is also calibrated and validated through real data, and the impact of fast-and-low-speed vehicles on traffic instability at ramp-merging area is analyzed. Numerical experiments show that the stochastic traffic flow model proposed in this paper well reproduces the traffic oscillations occurring in real traffic.