  Numerically we study the bulk current relaxation in percolative Random
Resistor cum Tunneling Network (RRTN) model through a first-passage route. The
RRTN considers an extra semi-classical barrier-crossing process over a voltage
threshold within a framework of classical RRN bond percolation model. We
identify the different temporal regimes of relaxation and corresponding
phenomenological time-scales, which fix up the extents of different regimes.
These time-scales were previously identified in refs. \cite{relax-physicaA,
aksubh}. We investigate on the distributions of these time-scales and observe
that there exists a perfect correlation among them in the thermodynamic limit.
We conclude that there exists a single time-scale which controls the RRTN
dynamics. The variation of mean first-passage time .vs. system size seems to be
due to sub-diffusive motion of charge carrier through the network.
