Cellular-automaton model with velocity adaptation in the framework of Kerner's three-phase traffic theory

In this paper, we propose a cellular automata (CA) model for traffic flow in the framework of Kerner’s three-phase traffic theory. We mainly consider the velocity-difference effect on the randomization of vehicles. The presented model is equivalent to a combination of two CA models, i.e., the Kerner-Klenov-Wolf (KKW) CA model and the Nagel-Schreckenberg (NS) CA model with slow-to-start effect. With a given probability, vehicle dynamical rules are changed over time randomly between the rules of the NS model and the rules of the KKW model. Due to the rules of the KKW model, the speed adaptation effect of three-phase traffic theory is automatically taken into account and our model can show synchronized flow. Due to the rules of the NS model, our model can show wide moving jams. The effect of “switching" from the rules of the KKW model to the rules of the NS model provides equivalent effects to the “acceleration noise" in the KKW model. Numerical simulations are performed for both periodic and open boundaries conditions. The results are consistent with the well-known results of the three-phase traffic theory published before.