A macroscopic traffic flow model considering the velocity difference between adjacent vehicles on uphill and downhill slopes

In this paper, we deduced a macroscopic traffic model on the uphill and downhill slopes by employing the transformation relation from microscopic variables to macroscopic ones based on a microscopic car-following model considering the velocity difference between adjacent vehicles. The angle [Formula: see text] of the uphill and downhill and the gravitational force have a great impact upon the stability of traffic flow. The linear stability analysis for macroscopic traffic model yielded the stability condition. The Korteweg–de Vries (KdV) equation is derived by nonlinear analysis and the corresponding solution to the density wave near the neutral stability line is obtained. By using the upwind finite difference scheme for simulation, the spatiotemporal evolution patterns of traffic flow on the uphill and downhill are attained. The unstable region is shrunken with slope of the gradient increasing and backward-traveling density waves gradually decrease and even disappear on uphill. Conversely, the unstable region on downhill is extended and density waves propagate quickly backward to the whole road with slope of the gradient increasing.

A Macroscopic Traffic Model based on Driver Reaction and Traffic Stimuli

A new macroscopic traffic flow model is proposed, which considers driver presumption based on driver reaction and traffic stimuli. The Payne–Whitham (PW) model characterizes the traffic flow based on a velocity constant C 0 which results in unrealistic density and velocity behavior. Conversely, the proposed model characterizes traffic behavior with velocities based on the distance headway. The performance of the proposed and PW models is evaluated over a 300 m circular road for an inactive bottleneck. The results obtained show that the traffic behavior with the proposed model is more realistic.