On cellular automata model of traffic flow with Lennard-Jones potential

By introducing the Lennard-Jones potential into the interaction of vehicles, a new cellular automata model of traffic flow is proposed, in which the fixed probability of randomisation of cellular automata is replaced by the state transition probability of cell sites. The proposed model considers that the driver is affected by the interactional potential of vehicles before him/her, and the decision-making process is related to the value of the interactional potential. The model is more suitable for the driver’s random decision-making process which is based on the stochastic behaviour of traffic flow. The fundamental diagram (flow density relationship) of the proposed model is obtained, and the complex traffic phenomenon is reproduced through numerical simulation.