Effect of the optimal velocity function on traffic phase transitions in lattice hydrodynamic models

The original lattice hydrodynamics models of traffic flow are extended to take into account the complex acceleration behavior of drivers. A new optimal velocity function which considers the stepwise acceleration effect and fits the observed data better is introduced. The stability conditions of these two models are obtained by using the linear stability theory. It is shown that the modified optimal velocity function has a remarkable influence on the neutral stability curve and the traffic phase transitions. In a certain vehicle’s density and driver’s sensitivity region, tri-stable states will occur. In addition, the properties of the multiple phases also depend on the asymmetry of the optimal velocity function and the stage number of multi-phase transitions is closely related to the turning points of the optimal velocity function. The validity and correctness of the analytical results is confirmed by numerical simulations.