  We address how the interplay between the finite availability and carrying
capacity of particles at different parts of a spatially extended system can
control the steady state currents and density profiles in the one-dimensional
current-carrying lanes connecting the different parts of the system. To study
this, we set up a minimal model consisting of two particle reservoirs of the
same finite carrying capacity connected by two equally sized anti-parallel
asymmetric exclusion processes (TASEP). We focus on the steady-state currents
and particle density profiles in the two TASEP lanes. The ensuing phases and
the phase diagrams, which can be remarkably complex, are parametrized by the
model parameters defining particle exchange between the TASEP lanes and the
reservoirs and the filling fraction of the particles that determine the total
resources available. These parameters may be tuned to make the densities of the
two TASEP lanes globally uniform or piece-wise continuous in the form of a
combination of a single localized domain wall and a spatially constant density
or a pair of delocalized domain walls. Our model reveals that the two
reservoirs can be preferentially populated or depopulated in the steady states.
