  We present a theoretical argument to derive a scaling law between the mean
translocation time $\tau$ and the chain length $N$ for driven polymer
translocation. This scaling law explicitly takes into account the pore-polymer
interactions, which appear as a correction term to asymptotic scaling and are
responsible for the dominant finite size effects in the process. By eliminating
the correction-to-scaling term we introduce a rescaled translocation time and
show, by employing both the Brownian Dynamics Tension Propagation theory
[Ikonen {\it et al.}, Phys. Rev. E {\bf 85}, 051803 (2012)] and molecular
dynamics simulations that the rescaled exponent reaches the asymptotic limit in
a range of chain lengths that is easily accessible to simulations and
experiments. The rescaling procedure can also be used to quantitatively
estimate the magnitude of the pore-polymer interaction from simulations or
experimental data. Finally, we also consider the case of driven translocation
with hydrodynamic interactions (HIs). We show that by augmenting the BDTP
theory with HIs one reaches a good agreement between the theory and previous
simulation results found in the literature. Our results suggest that the
scaling relation between $\tau$ and $N$ is retained even in this case.
