A New Traffic System on Driver Sensitivity and Safe Distance Headway

A new macroscopic traffic system is devised that observes the transition distance between the vehicles and driver sensitivity during traffic evolution. The driver sensitivity in this system is based on the traversed time over a 200 m road section and speed (velocity). In addition, the proposed system considers the safe distance headway as the distance between vehicles changes. An analogy system for vehicle flow behavior is devised from a spring–mass system with changes in traffic. The proposed system can characterize traffic evolution for small and large changes in density. Furthermore, the changes in the travel of traffic rearwards during congestion and forward during smooth flow are dependent on driver sensitivity, transition distance, and safe distance headway. The proposed traffic system is hyperbolic. The Payne Whitham traffic system is based on uniform constant velocity for different conditions, which characterizes traffic evolution unrealistically. The proposed traffic system and the Payne Whitham system are assessed over a 2000 m circular road for large changes in density in two examples. Both the Payne Whitham and proposed traffic systems are numerically implemented with the first order centered scheme in Matlab. The discretization stability of both systems is enforced with the Courant–Friedrich–Levy (CFL) condition. The proposed system with lower driver sensitivity evolves with larger changes, whereas the proposed system with larger density has smaller changes in density and velocity. The simulation results showed that the traffic evolution with the proposed system is more appropriate than with the Payne Whitham system.