  In one-dimensional random walks, the waiting time for each direction
transitions is the same, even in the presence of bias, as a consequence of the
microscopic-reversibility. We study the symmetry breaking of forward/ backward
transition times in a random walk on a lattice of two lanes. We find that
either transition times can be faster depending on the lattice's net current,
and the symmetry is recovered only at equilibrium. Our analysis suggests that
the forward/ backward transition times' asymmetry can be used as a measure of
deviation from the equilibrium of the system.
