Totally asymmetric simple exclusion process with a shortcut

In this paper, we study the interplay of a totally asymmetric simple exclusion process (TASEP) with a shortcut in its bulk under open boundary conditions. Two different models are introduced: (i) model A for molecular motor motion, and (ii) model B for vehicular traffic. The phase diagrams and density profiles of both models are studied. It is found that although the phase diagrams of both models can be classified into three regions, the phases corresponding to these regions and the phase boundaries between these regions are quite different in these two models. Moreover, the approximate stationary-state solutions of model A have been carried out and it is shown that the analytical results are in good agreement with the results of Monte Carlo simulations.