Analysis of the macroscopic effect of a driver’s desired velocity on traffic flow characteristics. (English) Zbl 07845831
Summary: 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.
MSC:
| 82-XX | Statistical mechanics, structure of matter |
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