Lattice hydrodynamic modeling with continuous self-delayed traffic flux integral and vehicle overtaking effect

This paper presents a new lattice hydrodynamic model with vehicle overtaking and the continuous self-delayed traffic flux integral. The linear stability condition of the model is derived through the linear stability analysis, which shows that the stable region can be enlarged by increasing the step of delay time. The modified Korteweg-de Vries (mKdV) equation is formulated through nonlinear analysis to describe the propagating behavior of traffic density wave near the critical point. The kink-anti-kink solution under different passing constants is also obtained. Results show that when the passing constant is lower than a threshold (Case I) that is associated with the delay time step, uniform flow and kink jam phase exhibits, and jamming transition occurs between the uniform flow and kink jam. When the passing constant exceeds the threshold (Case II), jamming transitions occur from uniform traffic flow to kink-Bando traffic wave through chaotic phase with decreasing sensitivity. Simulation examples verify that when the delay time increases from 0 to 0.6, the fluctuation amplitude of the traffic density is reduced from 0.07 to 0 even with exogenous initial disturbance, whereas under Case II, chaotic traffic flow appears when the density ranges from 0.18 to 0.31 and the delay time is 0.6.