Residence time estimates for asymmetric simple exclusion dynamics on strips

The target of our study is to approximate numerically and, in some particular physically relevant cases, also analytically, the residence time of particles undergoing an asymmetric simple exclusion dynamics on a two-dimensional vertical strip. The sources of asymmetry are twofold: (i) the choice of boundary conditions (different reservoir levels) and (ii) the strong anisotropy from a drift nonlinear in density with prescribed directionality. We focus on the effect of the choice of anisotropy on residence time. We analyze our results by means of two theoretical models, a Mean Field and a one-dimensional Birth and Death one. For positive drift we find a striking agreement between Monte Carlo and theoretical results. In the zero drift case we still find agreement as long as particles can freely escape the strip through the bottom boundary. Otherwise, the two models give different predictions and their ability to reproduce numerical results depends on the horizontal displacement probability. The topic is relevant for situations occurring in pedestrian flows or biological transport in crowded environments, where lateral displacements of the particles occur predominantly affecting therefore in an essentially way the efficiency of the overall transport mechanism.