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We explore how the interplay of finite availability, carrying capacity ofparticles at different parts of a spatially extended system and particlediffusion between them control the steady state currents and density profilesin a one-dimensional current-carrying channel connecting the different parts ofthe system. To study this, we construct a minimal model consisting of twoparticle reservoirs of finite carrying capacities connected by a totallyasymmetric simple exclusion process (TASEP). In addition to particle transportvia TASEP between the reservoirs, the latter can also directly exchangeparticles, modeling particle diffusion between them that can maintain a steadycurrent in the system. We investigate the steady state density profiles and theassociated particle currents in the TASEP lane. The resulting phases and thephase diagrams are quite different from an open TASEP, and are characterised bythe model parameters defining particle exchanges between the TASEP and thereservoirs, direct particle exchanges between the reservoirs, and the fillingfraction of the particles that determines the total resources available. Theseparameters can be tuned to make the density on the TASEP lane globally uniformor piecewise continuous, and can make the two reservoirs preferentiallypopulated or depopulated.

Availability, storage capacity, and diffusion: Stationary states of an asymmetric exclusion process connected to two reservoirs