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

TL;DR

This paper investigates traffic jam formation in a chain with a shortcut using the TASEP model, revealing conditions for coexistence phases, current behaviors, and implications for vehicular and molecular motor traffic.

Contribution

It provides a detailed analysis of traffic jam conditions in a chain with a shortcut, including phase coexistence and current distribution, using effective rates and domain wall theory.

Findings

Existence of coexistence phase with delocalized domain wall at any external rate in maximum current phase.

Density profiles and coexistence features are well described by domain wall theory, depending mainly on shortcut current.

Counterintuitively, longer shunted segments can have higher current than the shortcut.

Abstract

The appearance of traffic jams on chains with a shunted section between two simple chain segments in the maximum current phase is studied in the framework of the Totally Asymmetric Simple Exclusion Process. The conditions for the occurrence of this phenomenon are investigated both within the effective rates approximation and numerically for arbitrary length of the shortcut. The problem is interesting on its own because the conditions for coexistence of low- and high density phases are essentially different from those for a simple chain between two reservoirs. Our main results are: (1) For 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 negligible inter-chain correlations, they depend only on the current through the shortcut; (3) The model displays an unexpected feature: the current through the longer shunted segment is larger than the current through the shortcut; (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.