Transport at a complex multiple-input-multiple-output TASEP junction

The Totally Asymmetric Simple Exclusion Process (TASEP) is widely used to study transport on networks. Here, we focus on a multiple-input-multiple-output (MIMO) junction with complex kinetic rules and develop an innovative numerical method to solve the equation for mean-field current conservation at the junction using Constrained Optimisation, that we supplement with stochastic simulations following a Gillespie algorithm. We observe that lattices with the same ratio of upstream to downstream segments have the same phase diagrams, in the absence of bias, and in the absence of bottleneck effect. As soon as a bias is introduced on the side of the junction with fewer segments, a bottleneck effect arises, leading to a reduction of the current on the segments and at the junction, and a change of the junction current–density relation from quadratic to piece-wise quasi-linear. In the absence of bias, the bottleneck effect arises in particular in lattices where the rates of absorption into and pumping out of the junction lie under a certain threshold, which is dependent on the number of upstream and downstream segments, as well as the junction density. As biases are introduced on either or both of the upstream and downstream segments, a very complex phenomenology emerges on the overall lattice, involving a combinatorial explosion of the phases. Furthermore, particle–hole symmetry, well-established for a simple TASEP segment, extends here as well, enabling us to recover the phase diagrams for lattices with opposite configurations.