Flow overshooting in crossing flow of lattice gas

We study the lattice gas flow of two components of biased-random walkers at a crossing under a periodic boundary. The lattice gas mixture consists of two components of particles (walkers) in which one component of particles moves north and the other component of particles moves east. The current (flow) increases with ρx (density of the east-bound particles) at low density and displays overshooting at an intermediate density. The flow overshooting occurs only for a certain range of ρy (density of the north-bound particles). Then clogging occurs and the current saturates. Furthermore, when the density is high, the current decreases with increasing density. The overshooting shown in the current-density (fundamental) diagram is due to the formation of an unstable oscillating jam just before clogging occurs. It is shown that flow overshooting does not occur in unidirectional flow through a porous medium but occurs in unidirectional flow through a group of Brownian particles.