Asymmetric exclusion processes with fixed resources: Reservoir crowding and steady states

We study the reservoir crowding effect by considering the nonequilibrium steady states of an asymmetric exclusion process (TASEP) coupled to a reservoir with fixed available resources and dynamically coupled entry and exit rate. We elucidate how the steady states are controlled by the interplay between the coupled entry and exit rates, both being dynamically controlled by the reservoir population, and the fixed total particle number in the system. The TASEP can be in the low-density, high-density, maximal current, and shock phases. We show that such a TASEP is different from an open TASEP for all values of available resources: here the TASEP can support only localized domain walls for any (finite) amount of resources that do not tend to delocalize even for large resources, a feature attributed to the form of the dynamic coupling between the entry and exit rates. Furthermore, in the limit of infinite resources, in contrast to an open TASEP, the TASEP can be found in its high-density phase only for any finite values of the control parameters, again as a consequence of the coupling between the entry and exit rates.