One-transit paths and steady-state of a non-equilibrium process in a   discrete-time update
  We have shown that the partition function of the Asymmetric Simple Exclusion Process with open boundaries in a sublattice-parallel updating scheme is equal to that of a two-dimensional one-transit walk model defined on a diagonally rotated square lattice. It has been also shown that the physical quantities defined in these systems are related through a similarity transformation. 
Vahid Fayaz, Farhad H. Jafarpour, Seyedeh Raziyeh Masharian, Somayeh   Zeraati
cond-mat.stat-mech cond-mat.dis-nn