Reservoir crowding in a dynamically disordered bidirectional system with narrow entrances

Motivated by the presence of imperfections in the complex processes of vehicular traffic and intracellular transport, we investigate a two-lane dynamically disordered system with narrow entrances. The movement of the particles is obstructed by the presence of defects that bind/unbind stochastically from each site. A global constraint on both the number of particles and defects is considered which is characterized by individual reservoirs. Specifically, the particle reservoir features reservoir crowding, which affects the entry-exit rates of particles. We analyzed the model within the mean-field framework and examined complex phenomena such as stationary phase diagrams, particle densities and spontaneous symmetry breaking. The role of the various parameters: binding/unbinding rate of defects, entry-exit rates of the particles, hopping rate of particles in the presence of defect and the number of particles/defects, is thoroughly examined. Our results display a rich behaviour, emphasizing the influence of reservoir crowding, resulting in both symmetric and asymmetric phases. Another important consequence is the back-and-forth transition and the persistence of a localized domain wall in the system, even for abundant particle resources. All theoretical findings are validated by extensive Monte Carlo simulations.