  We study the nonequilibrium steady states of an asymmetric exclusion process
(TASEP) coupled to a reservoir of unlimited capacity. We elucidate how the
steady states are controlled by the interplay between the reservoir population
that dynamically controls both the entry and exit rates of the TASEP, and the
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 localised domain walls for any (finite) amount of
resources as opposed to delocalised domain walls in open TASEPs. Furthermore,
in the limit of infinite resources, the TASEP can be found in its high density
phase only for any finite values of the control parameters, in contrast to an
open TASEP.
