Frozen shuffle update for an asymmetric exclusion process with open   boundary conditions
  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. 
C. Appert-Rolland, J. Cividini and H.J. Hilhorst
cond-mat.stat-mech physics.soc-ph