Jamming transition of pedestrian traffic at a crossing with open boundaries

Pedestrian traffic at a crossing is investigated under the open boundary condition by the use of the lattice gas model of biased random walkers without the back step. The four types of walkers interact with each other at the crossing where there are random walkers going to the right, left, up, and down. It is found that a dynamical jamming transition from the moving state at low density to the stopped state at high density occurs at the critical density. The transition point depends on the strength of drift and decreases with increasing drift. The transition point does not depend on the length of roads connecting the crossing for the long road. Also, the pedestrian traffic with two types of walkers is studied where there are random walkers going to the right and up. It is compared with the pedestrian traffic with the four types of random walkers.