Jamming transition in two-dimensional pedestrian traffic

Jamming transitions of pedestrian traffic are investigated under the periodic boundary condition on the square lattice by the use of the lattice gas model of biased random walkers without the back step. The two cases are presented: the one with two types of walkers and the other with four types of walkers. In the two types of walkers, the first is the random walker going to the right and the second is the random walker going up. In the four types of walkers, the first, second, third, and fourth are, respectively, the random walkers going to the right, left, up, and down. It is found that the dynamical jamming transitions occur at the critical densities. The transition points do not depend on the system size for large system but depend strongly on the strength of drift. The jamming transitions are compared with that obtained by the cellular automaton model of car traffic.