Figure 1. Sketch of the model.

A particle moves to the front empty site with probability p if the rear site is empty(configuration I). Otherwise, if the rear site is occupied, the particle moves to the front empty site with probability q (configuration II). In the case of p = q, the model reduces to the basic ASEP. The filled circles indicate sites occupied by particles, and the dotted-open circles denote empty sites. The absence of circles means the site is empty or occupied.