One-dimensional cellular automaton model of traffic flow based on car-following idea

An improved one-dimensional CA (Cellular Automaton) traffic model was proposed to describe the highway traffic under the periodic boundary conditions. The model was based on the idea of the car-following model, which claimed that the motion of a vehicle at one time step depended on both its headway and the synchronous motion of the front vehicle, thus including indirectly the influence of its sub-neighboring vehicle. In addition, the so-called safety distance was introduced to consider the deceleration behavior of vehicles and the stochastic factor was taken into account by introducing the deceleration probability. Meanwhile, the conditional deceleration in the model gave a better description of the phenomena observed on highways. It is found that there exists the metastability and hysteresis effect of traffic flow in the neighborhood of critical density under different initial conditions. Since this model gives a reasonable depiction of the motion of a single vehicle, it is easy to be extended to the case of traffic flow under the control of traffic lights in cities.