Jamming and freezing transitions in CA model for facing pedestrian traffic with a soft boundary

We present a bi-directional cellular automaton (CA) model for facing traffic of pedestrians on a footway with a soft boundary. Walkers are allowed to go across a soft boundary to avoid congestion. The soft boundary effect is taken into account in addition to the excluded-volume effect and bi-directionality. The CA model is not stochastic but deterministic. We study the effect of the soft boundary on the jamming and freezing transitions. We show that the dynamical phase transition has a strong dependence on the soft boundary. There exist four traffic states: the free traffic, jammed traffic 1, jammed traffic 2, and frozen state. At the frozen state, all pedestrians stop and are prevented from moving. At the dynamical transitions, the pedestrian flow changes from the free traffic, through the jammed traffics 1 and 2, to the frozen state.