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

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