A Markov Process Inspired Cellular Automata Model of Road Traffic
  To provide a more accurate description of the driving behaviors in vehicle queues, a namely Markov-Gap cellular automata model is proposed in this paper. It views the variation of the gap between two consequent vehicles as a Markov process whose stationary distribution corresponds to the observed distribution of practical gaps. The multiformity of this Markov process provides the model enough flexibility to describe various driving behaviors. Two examples are given to show how to specialize it for different scenarios: usually mentioned flows on freeways and start-up flows at signalized intersections. The agreement between the empirical observations and the simulation results suggests the soundness of this new approach. 
Fa Wang, Li Li, Jianming Hu, Yan Ji, Danya Yao, Yi Zhang, Xuexiang   Jin, Yuelong Su, Zheng Wei