  Quantum transport simulations often use explicit, yet finite, electronic
reservoirs. These should converge to the correct continuum limit, albeit with a
trade-off between discretization and computational cost. Here, we study this
interplay for extended reservoir simulations, where relaxation maintains a bias
or temperature drop across the system. Our analysis begins in the
non-interacting limit, where we parameterize different discretizations to
compare them on an even footing. For many-body systems, we develop a method to
estimate the relaxation that best approximates the continuum by controlling
virtual transitions in Kramers' turnover for the current. While some
discretizations are more efficient for calculating currents, there is little
benefit with regard to the overall state of the system. Any gains become
marginal for many-body, tensor network simulations, where the relative
performance of discretizations varies when sweeping other numerical controls.
These results indicate that a given reservoir discretization may have little
impact on numerical efficiency for certain computational tools. The choice of a
relaxation parameter, however, is crucial, and the method we develop provides a
reliable estimate of the optimal relaxation for finite reservoirs.
