Analysis of the macroscopic effect of a driver’s desired velocity on traffic flow characteristics

In Prigogine's traffic kinetic model, the expected velocity of each driver is assumed to be independent of time, and its relaxation term is ignored. In Paveri–Fontana’s model, the vehicle accelerates to the desired velocity by means of a relaxation term. Méndez’s model assumed that the desired velocity is proportional to the instantaneous velocity, reflecting that all drivers want to drive at a higher velocity, which is a characteristic of aggressive drivers. In order to restrain the character of drivers, considering the relationship between a driver’s desired velocity and the surrounding environment and local instantaneous velocity, a new relaxation process is adopted, which describes that the desired velocity is adaptively adjusted toward the local equilibrium velocity within the relaxation time. We use Chapman-Enskog method and Grad’s moments method to derive the Navier-Stokes traffic equation. The stability condition is obtained by the linear stability analysis. Compared with the steady situation of both Kerner–Konhäuser model and Helbing’s model, it is shown that the extended continuum model has the ability to simulate stop-and-go traffic under medium and high density. Numerical simulation results show that the extended continuum model has a better control effect of traffic congestion than the Paveri–Fontana equation. Finally, the rationality of the extended continuum model is verified by simulations of partially reduced lane traffic and high-density traffic flow.