  A non-equilibrium particle transport model, the totally asymmetric exclusion
process, is studied on a one-dimensional lattice with a hierarchy of fixed
long-range connections. This model breaks the particle-hole symmetry observed
on an ordinary one-dimensional lattice and results in a surprisingly simple
phase diagram, without a maximum-current phase. Numerical simulations of the
model with open boundary conditions reveal a number of dynamic features and
suggest possible applications.
