A cellular automaton traffic flow model between the Fukui-Ishibashi and Nagel-Schreckenberg models

We propose and study a new one-dimensional traffic flow cellular automaton (CA) model of high speed vehicles with the Fukui-Ishibashi-type acceleration for all cars and the Nagel-Schreckenberg-type (NS) stochastic delay only for the cars following the trail of the car ahead. The main difference in the delay scenario between the new model and the NS model is that a car with spacing ahead longer than the velocity limit $M$ may not be delayed in the new model. By using a car-oriented mean field theory, we derive the fundamental diagrams of the average speed as the function of car density analytically. Our theoretical results are in excellent agreement with numerical simulations.