Stability analysis of feedforward anticipation optimal flux difference in traffic lattice hydrodynamic theory

• Published in: Communications in nonlinear science & numerical simulation 2018-03, Vol.56, p.287-295
• Main Authors: Sun, Di-Hua, Zhang, Geng, Zhao, Min, Cheng, Sen-Lin, Cao, Jian-Dong
• Format: Article
• Language: English
• Subjects: Anticipation optimal flux difference; Automobile driving; Computer simulation; Critical point; Cyber-physical systems; Fluid mechanics; Flux; Jamming; Lattice hydrodynamic model; mKdV equation; Perturbation methods; Propagation; Stability analysis; Traffic flow; Traffic models; Traffic volume; Wave propagation
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2017.08.004

•A new traffic lattice hydrodynamic model is proposed by firstly considering driver's anticipation optimal flux difference effect in light of feedforward control theory.•Linear stability analysis is conducted to reveal the impact of driver's anticipation effect on traffic stability.•Nonlinear reductive perturbation method is used to uncover the nonlinear characteristics of traffic density waves.•The driver's feedforward anticipation optimal flux difference effect can enhance the stability of traffic flow and should be considered in real traffic. Recently, the influence of driver's individual behaviors on traffic stability is research hotspot with the fasting developing transportation cyber-physical systems. In this paper, a new traffic lattice hydrodynamic model is proposed with consideration of driver's feedforward anticipation optimal flux difference. The neutral stability condition of the new model is obtained through linear stability analysis theory. The results show that the stable region will be enlarged on the phase diagram when the feedforward anticipation optimal flux difference effect is taken into account. In order to depict traffic jamming transition properties theoretically, the mKdV equation near the critical point is derived via nonlinear reductive perturbation method. The propagation behavior of traffic density waves can be described by the kink–antikink solution of the mKdV equation. Numerical simulations are conducted to verify the analytical results and all the results confirms that traffic stability can be enhanced significantly by considering the feedforward anticipation optimal flux difference in traffic lattice hydrodynamic theory.