In this paper we rationalize relevant features of totally asymmetric simple-exclusion processes on topologies more complex than a single segment. We present a mean-field framework, exploiting the previously introduced notion of effective rates, which we express in terms of the average particle density on explicitly introduced junction sites. It allows us to construct the phase behavior as well as the current-density characteristic from well-known results for a linear totally asymmetric simple-exclusion-process segment in a very systematic and generic way. We validate the approach by studying a fourfold vertex in all variations in the number of entering/exiting segments and compare our predictions to simulation data. Generalizing the notion of particle-hole symmetry to take into account the topology at a junction shows that the average particle density at the junction constitutes a relevant directly observable parameter which gives detailed insight into the transport process. This is illustrated by a complete study of a simple network with figure-of-eight topology. Finally we generalize the approach to handle rate bias at a junction and discuss the surprisingly rich phenomenology of a biased figure-of-eight structure. This example highlights that the proposed framework is generic and readily extends to other topologies.

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We investigate a totally asymmetric simple exclusion process (TASEP) on a periodic hexagonal lattice with a single unit cell. We first explain the resulting stationary density profiles and the resulting fundamental current–density relation in terms of mean-field arguments. For intermediate overall densities, transport through one of the segments saturates in a maximum current phase, whereas the others develop domain walls of fixed height but fluctuating position. Via kinetic Monte Carlo simulations we focus on and fully characterize their non-equilibrium and stochastic phenomenology. We invoke a picture of anticorrelated domain wall dynamics, which we visualize as a diffusing obstruction of constant size (‘jam’). The role of the boundary conditions is discussed by comparing the periodic lattice carrying a fixed number of particles to a system coupled to reservoirs at open boundaries which is periodic only on average. We highlight the differences in their dynamics based on a novel visualization of domain wall motion at an intermediate ‘mesoscopic’ timescale.