Asymmetric simple exclusion process on chains with a shortcut.

We consider the asymmetric simple exclusion process (TASEP) on an open network consisting of three consecutively coupled macroscopic chain segments with a shortcut between the tail of the first segment and the head of the third one. The model was introduced by Y.-M. Yuan et al. [J. Phys. A 40, 12351 (2007)] to describe directed motion of molecular motors along twisted filaments. We report here unexpected results which revise the previous findings in the case of maximum current through the network. Our theoretical analysis, based on the effective rates' approximation, shows that the second (shunted) segment can exist in both low- and high-density phases, as well as in the coexistence (shock) phase. Numerical simulations demonstrate that the last option takes place in finite-size networks with head and tail chains of equal length, provided the injection and ejection rates at their external ends are equal and greater than one-half. Then the local density distribution and the nearest-neighbor correlations in the middle chain correspond to a shock phase with completely delocalized domain wall. Upon moving the shortcut to the head or tail of the network, the density profile takes a shape typical of a high- or low-density phase, respectively. Surprisingly, the main quantitative parameters of that shock phase are governed by a positive root of a cubic equation, the coefficients of which linearly depend on the probability of choosing the shortcut. Alternatively, they can be expressed in a universal way through the shortcut current. The unexpected conclusion is that a shortcut in the bulk of a single lane may create traffic jams.