  We introduce a new update algorithm for exclusion processes, more suitable
for the modeling of pedestrian traffic. Pedestrians are modeled as hard-core
particles hopping on a discrete lattice, and are updated in a fixed order,
determined by a phase attached to each pedestrian. While the case of periodic
boundary conditions was studied in a companion paper, we consider here the case
of open boundary conditions. The full phase diagram is predicted analytically
and exhibits a transition between a free flow phase and a jammed phase. The
density profile is predicted in the frame of a domain wall theory, and compared
to Monte Carlo simulations, in particular in the vicinity of the transition.
