Research On Stochastic Behavior Of Traffic Flow Based On Interactional Potential

Along with the increase of population and vehicles, the development of road is difficult to satisfy the need of vehicular traffic. The programming, management and control of traffic are becoming a critical problem. In the actual traffic, the driver always affected by the stochastic factors such as vehicles in front of him, road surroundings etc. The decision of accelerating and deceleration is making out by the value of interactional potential energy. The main models in existing are almost deterministic, can not describe the stochastic behavior of high density traffic system. Therefore, in this dissertation, the research on stochastic nonlinear behavior of traffic system has been carry out. Based on the Ising model of Markov random field method, the particle interaction model, and the Arrhenius model, the interaction potential functions of the effects of random factors such as the related vehicles are constructed. The model of traffic system based on random interaction potential function is established in theory, and the random behavior and evolution mechanism of the traffic system are explored.In view of the random phenomena and nonlinear behavior of the traffic flow in the traffic system of single lane highway, this dissertation mainly studies the following aspects:(1)Considering the fact that in actual traffic, the driver is subjected to the interaction of multiple vehicles in front of him/her, and the decision process of acceleration and deceleration is dynamicly made out by the interactional potential of the vehicles in front of the driver, based on the Ising model and the Arrhenius microscopic dynamic models, a new cellular automata model of traffic flow with variable slow probability is proposed, which improve the fixed slowdown probability of the existing cellular automaton model with the dynamic changed stochastic slowdown probability. Through numerical simulation, the complex behavior of high density traffic flow is simulated and reconstructed.(2) In consideration of the fact that the different distance of the vehicles to the driver’s have different influence, by introducing the weighting coefficient into the look-ahead potential and endowing the potential of vehicle closer to itself with a greater weight, a novel traffic flow model with weighted look-ahead potential is presented. The simulation results show that the weighting coefficient has an obvious effect on high-density traffic flux, and the weighted model is more conducive to keeping high traffic flux and road capacity while maintaining a high traffic density.(3) The influence of front vehicles is a process related to the distance between them. By introducing the Lennard-Jones continuous potential function of molecular dynamics, an new traffic flow model based on Lennard-Jones is proposed. In the proposed model, the continuous potential function of the Lennard-Jones is used to improve the slowdown probability of the cellular automaton traffic flow models. The driver’s random decision-making process based on the vehicle and road surroundings in front of him in actual traffic is well described by this model.(4) Given continuous influence of vehicle speed and distance on traffic flow, by constructing a continuous potential function related to vehicle speed and distance, two new models of the cellular automaton traffic flow model based on continuous interaction potential are proposed, which are respectively optimization safe distance dependent potential function model and driver response strength correlation potential function model. Through numerical simulations, the proposed model has a greater traffic density and traffic flow, and a better representation of high density traffic flow complex behavior.(5) Based on the discrete and continuous interaction potential function of the above mentioned above, a random force model of vehicle interaction with potential function is established. The stochastic force is introduced into the vehicle dynamics model, and the dynamic models with stochastic force are constructed. The concrete expression of the random force model and the concrete expression of the stochastic dynamic equation are discussed in detail. Based on Lyapunov stability theory, the linear stability analysis of the dynamic models are carried out, and the stability conditions are obtained.The results of this dissertation will enrich and develop the dynamic theory of traffic system, and provide the programming, management, control of traffic, and engineering application with theoretic foundation.