An improved car-following model considering the space relaxation effect

Gap between car-following(CF) models and real traffic system is a tough question, which directly affects the accuracy on describing traffic evolution. In general, the sensitivity parameter of CF models is considered as a constant. However in real traffic system, when the space between two successive vehicles is sufficiently large, the following vehicle is insensitive to space variation. To fill this gap, the space relaxation effect is explored and expressed in this paper. Firstly, data segments which record acceleration, velocity difference(VD) and space headway deviation(SHD) from steady-state to unsteady-state are extracted from next generation simulation(NGSIM) dataset. By employing the discrete Fréchet distance(DFD) algorithm, the similarity of temporal curves in each data segment is analyzed so that the space relaxation effect is explored. Base on this fact, an improved CF model is proposed and linear stability of model is strictly analyzed. Then, numerical simulations are carried out. Following vehicles’ acceleration, space headway(SH), velocity are exhibited and analyzed in detail. Comparing with full velocity difference model(FVDM), our improved model can express a smoother acceleration adjustment process of subject vehicle under relatively large SH. Finally, 50 times data fitting experiments are conducted. Actual velocity and trajectory of following vehicle in every instant is compared with the values that computed by FVDM and our improved models respectively. The results reveal that space relaxation effect is actually existent in real traffic system. Our improved model can accurately depict the traffic evolution by considering this effect.