Analytical investigation of the boundary-triggered phase transition dynamics in a cellular automata model with a slow-to-start rule

Previous studies suggest that there are three different jam phases in the cellular automata automaton model with a slow-to-start rule under open boundaries. In the present paper, the dynamics of each free-flow-jam phase transition is studied. By analysing the microscopic behaviour of the traffic flow, we obtain analytical results on the phase transition dynamics. Our results can describe the detailed time evolution of the system during phase transition, while they provide good approximation for the numerical simulation data. These findings can perfectly explain the microscopic mechanism and details of the boundary-triggered phase transition dynamics.