Congestion fronts of diffusing particles

We study two new models of two particle species invading a surface from opposite sides. Collisions of particles of different species lead to the formation of congestion fronts. One of the models implements a reversible process whereas in the other model the congestion front forms irreversibly. For both models we find that the congestion fronts are self-affine but with different roughness exponents. For low densities the system does not congest and we find a phase transition between a phase of freely moving particles and a congestion phase.