Analytical Studies on a Modified Nagel-Schreckenberg Model with the   Fukui-Ishibashi Acceleration Rule
  We propose and study a one-dimensional traffic flow cellular automaton model of high-speed vehicles with the Fukui-Ishibashi-type (FI) acceleration rule for all cars, and the Nagel-Schreckenberg-type (NS) stochastic delay mechanism. By using the car-oriented mean field theory, we obtain analytically the fundamental diagrams of the average speed and vehicle flux depending on the vehicle density and stochastic delay probability. Our theoretical results, which may contribute to the exact analytical theory of the NS model, are in excellent agreement with numerical simulations. 
Chuan-Ji Fu, Chuan-Yang Yin, Tao Zhou, Bo Hu, Bing-Hong Wang, and Kun   Gao