  The Random Resistor cum Tunneling Network (RRTN) model was proposed from our
group by considering an extra phenomenological (semi-classical) tunneling
process into a classical RRN bond percolation model. We earlier reported about
early-stage two inverse power-laws, followed by large time purely exponential
tail in some of the RRTN macroscopic current relaxations. In this paper, we
investigate on the broader perspective of current relaxation. We present here
an analytical argument behind the strong convergence (irrespective of initial
voltage configuration) of the bulk current towards its steady-state, mapping
the problem into a special kind of Gauss-Seidel method. We find two
phenomenological time-scales (referred as $\tau_t$ and $\tau_s$), those emerge
from the variation of macroscopic quantities during current dynamics. We show
that not both, only one of them is independent. Thus there exists a {\it
single} scale in time which controls the entire dynamics.
