Feedback and fluctuations in a totally asymmetric simple exclusion process with finite resources

We revisit a totally asymmetric simple exclusion process (TASEP) with open boundaries and a global constraint on the total number of particles (Adams et al 2008 J. Stat. Mech. P06009). In this model, the rate of entry of particles into the lattice depends on the number available in the reservoir. Thus, the total occupation on the lattice feeds back into its filling process. Although a simple domain wall theory provided reasonably good predictions for Monte Carlo simulation results for certain quantities, it did not account for the fluctuations of this feedback. We generalize the previous study and find dramatically improved predictions for, e. g., the density pro. le on the lattice, and provide a better understanding of the phenomenon of 'shock localization'.