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We study the nonequilibrium steady states of an asymmetric exclusion process(TASEP) coupled to a reservoir of unlimited capacity. We elucidate how thesteady states are controlled by the interplay between the reservoir populationthat dynamically controls both the entry and exit rates of the TASEP, and thetotal particle number in the system. The TASEP can be in the low density, highdensity, maximal current and shock phases. We show that such a TASEP isdifferent from an open TASEP for all values of available resources: here, theTASEP can support only localised domain walls for any (finite) amount ofresources as opposed to delocalised domain walls in open TASEPs. Furthermore,in the limit of infinite resources, the TASEP can be found in its high densityphase only for any finite values of the control parameters, in contrast to anopen TASEP.

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