  In a model of $N$ volume-excluding spheres in a $d$-dimensional tube, we
consider how differences between particles in their drift velocities,
diffusivities, and sizes influence the steady state distribution and axial
particle current. We show that the model is exactly solvable when the
geometrical constraints prevent any particle from overtaking every other -- a
notion we term quasi-one-dimensionality. Then, due to a ratchet effect, the
current is biased towards the velocities of the least diffusive particles. We
consider special cases of this model in one dimension, and derive the exact
joint gap distribution for driven tracers in a passive bath. We describe the
relationship between phase space structure and irreversible drift that makes
the quasi-one-dimensional supposition key to the model's solvability.
