A new stochastic cellular automaton model on traffic flow and its   jamming phase transition
  A general stochastic traffic cellular automaton (CA) model, which includes slow-to-start effect and driver's perspective, is proposed in this paper. It is shown that this model includes well known traffic CA models such as Nagel-Schreckenberg model, Quick-Start model, and Slow-to-Start model as specific cases. Fundamental diagrams of this new model clearly show metastable states around the critical density even when stochastic effect is present. We also obtain analytic expressions of the phase transition curve in phase diagrams by using approximate flow-density relations at boundaries. These phase transition curves are in excellent agreement with numerical results. 
Satoshi Sakai, Katsuhiro Nishinari and Shinji Iida