Abstract
To model the car-following behavior more accurately, we carried out the molecular similarity analysis between the vehicles on the road and the inert gas system, comparing vehicles with microscopic particles in long and narrow pipes. The complex car-following interaction behavior is simplified into a dynamic process of the follower car that is constantly seeking to maintain the required safety distance from the leading vehicle. Through mathematical derivation of the Lennard–Jones potential function suitable for thermodynamic analysis of inert gas systems, the influence of each variable on the potential energy is clarified, and the existing problems of the existing molecular car-following model are analyzed, referring to the general Lennard–Jones potential function to build the vehicle interaction potential function. Considering the impact of the road wall potential generated by the lane boundary, a car-following model based on Lennard–Jones interaction potential is presented. The simulation test results show that compared with the existing molecular car-following model and IDM model, the average absolute error and root mean square error of the vehicle acceleration results obtained by this model and the actual data are lower, which proves that the vehicle is based on the Lennard–Jones interaction potential. The vehicle-following model based on Lennard–Jones interaction potential has a better fitting effect on the real vehicle-following behavior.
Highlights
Vehicle-following behavior is the basic element of microtraffic flow characteristics, and the research on it has been the focus of transportation discipline since the 1950s
E 6–12 potential is only a special calibration form of the Lennard–Jones potential, which is a narrow Lennard–Jones potential. e 6–12 potential is a classic pair-potential function in molecular dynamics and thermodynamic modeling. It is the prototype of the vehicle interaction potential function for building and improving the car-following model based on molecular dynamics in literature [10, 18]
Referring to the generalized Lennard–Jones potential function in the form of equation (5), the power n and m of the attraction and repulsive terms are set as the parameters to be calibrated in the model to build the vehicle interaction potential function
Summary
Vehicle-following behavior is the basic element of microtraffic flow characteristics, and the research on it has been the focus of transportation discipline since the 1950s. Some scholars have compared the dynamic characteristics of vehicles in the road with those of microparticles to study the car-following behavior. Li et al [9] built a molecular dynamics-based car-following model based on the vehicle-following molecular dynamics model using the presented vehicle interaction potential. E car-following model based on molecular dynamics and its improved model use the Lennard–Jones 6–12 potential function to study the car-following behavior, while the Lennard–Jones 6–12 potential function is essentially a potential function applicable to the thermodynamics of microparticles in fluids. Erefore, this study considers the differences of motion conditions between the microparticles and the vehicle, deeply analyses the similar relationship between the microparticles and vehicle interaction, builds a potential function more suitable for reflecting the vehicle-following behavior, and establishes the corresponding vehicle-following dynamic model
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