Totally asymmetric simple exclusion process with one or two shortcuts

In this paper, the operation of totally asymmetric simple exclusion process with one or two shortcuts under open boundary conditions is discussed. Using both mathematical analysis and numerical simulations, we have found that, according to the method chosen by the particle at the bifurcation, the model can be separated into two different situations which lead to different results. The results obtained in this paper would be very useful in the road building, especially at the bifurcation of the road.