On the appearance of traffic jams in a long chain with a shortcut in the bulk

Abstract

The Totally Asymmetric Simple Exclusion Process (TASEP) is studied on open long chains with a shunted section between two simple chain segments in the maximum current phase. The reference case, when the two branches are chosen with equal probability, is considered. The conditions for the occurrence of traffic jams and their properties are investigated both within the effective rates approximation and by extensive Monte Carlo simulations for arbitrary length of the shortcut. Our main results are: (1) For any length of the shortcut and any values of the external rates in the domain of the maximum current phase, there exists a position of the shortcut where the shunted segment is in a phase of coexistence with a completely delocalized domain wall; (2) The main features of the coexistence phase and the density profiles in the whole network are well described by the domain wall theory. Apart from the small inter-chain correlations, they depend only on the current through the shortcut; (3) The model displays unexpected features: (a) the current through the longer shunted segment is larger than the current through the shortcut, and (b) the delocalized domain wall in the coexistence phase of the long shunted segment induces similar behavior even in shortcuts containing a small number of sites; (4) From the viewpoint of vehicular traffic, most comfortable conditions for the drivers are provided when the shortcut is shifted downstream from the position of coexistence, when both the shunted segment and the shortcut exhibit low-density lamellar flow. Most unfavorable is the opposite case of upstream shifted shortcut, when both the shunted segment and the shortcut are in a high-density phase describing congested traffic of slowly moving cars. The above results are relevant also to phenomena like crowding of molecular motors moving along twisted protofilaments.