Cellular Automaton Model for One Dimensional Traffic Flow with Gradual Acceleration and Stochastic Delay: Analytical Approach

A new cellular automaton (CA) model for traffic flow, which is situated between Nagel-Schreckenberg (NS) type and Fukui-Ishibashi (FI) type, is defined and studied. This new model adopts the gradual acceleration scenario for all cars as NS model and the stochastic delay scenario for only the car with speed limit as FI model. It is proved that the fundamental diagram for the new model is exactly same with that for FI model. This means that if the acceleration scenario of the FI traffic flow model , in which a car may increase in velocity rapidly from zero to the velocity limit M or the maximum velocity permitted by empty spacing ahead, is changed to gradual way in which the velocity of a car may increase by only one unit at most in one time step, the asymptotic steady state behavior of traffic flow will not be changed by interaction between cars and the self-organization evolution of the traffic flow.