  The Transiting Exoplanet Survey Satellite will conduct a 2-year long
wide-field survey searching for transiting planets around bright stars. Many
TESS discoveries will be amenable to mass characterization via ground-based
radial velocity measurements with any of a growing suite of existing and
anticipated velocimeters in the optical and near-infrared. In this study we
present an analytical formalism to compute the number of radial velocity
measurements---and hence the total observing time---required to characterize RV
planet masses with the inclusion of either a white or correlated noise activity
model. We use our model to calculate the total observing time required to
measure all TESS planet masses from the expected TESS planet yield while
relying on our current understanding of the targeted stars, stellar activity,
and populations of unseen planets which inform the expected radial velocity
precision. We also present specialized calculations applicable to a variety of
interesting TESS planet subsets including the characterization of 50 planets
smaller than 4 Earth radii which is expected to take as little as 60 nights of
observation. Although, the efficient RV characterization of such planets
requires a-priori knowledge of the `best' targets which we argue can be
identified prior to the conclusion of the TESS planet search based on our
calculations. Our results highlight the comparable performance of optical and
near-IR spectrographs for most planet populations except for Earths and
temperate TESS planets which are more efficiently characterized in the near-IR.
Lastly, we present an online tool to the community to compute the total
observing times required to detect any transiting planet using a user-defined
spectrograph.
