  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.
