  Radial-velocity follow-up of stars harbouring transiting planets detected by
TESS is expected to require very large amounts of expensive telescope time in
the next few years. Therefore, scheduling strategies should be implemented to
maximize the amount of information gathered about the target planetary systems.
We consider myopic and non-myopic versions of a novel uniform-in-phase
scheduler, as well as a random scheduler, and compare these scheduling
strategies with respect to the bias, accuracy and precision achieved in
recovering the mass and orbital parameters of transiting and non-transiting
planets. This comparison is carried out based on realistic simulations of
radial-velocity follow-up with ESPRESSO of a sample of 50 TESS target stars,
with simulated planetary systems containing at least one transiting planet with
a radius below $4R_{\oplus}$. Radial-velocity datasets were generated under
reasonable assumptions about their noise component, including that resulting
from stellar activity, and analysed using a fully Bayesian methodology. We find
the random scheduler leads to a more biased, less accurate, and less precise,
estimation of the mass of the transiting exoplanets. No significant differences
are found between the results of the myopic and non-myopic implementations of
the uniform-in-phase scheduler. With only about 22 radial velocity measurements
per dataset, our novel uniform-in-phase scheduler enables an unbiased (at the
level of 1\%) measurement of the masses of the transiting planets, while
keeping the average relative accuracy and precision around 16\% and 23\%
respectively. The number of non-transiting planets detected is similar for all
the scheduling strategies considered, as well as the bias, accuracy and
precision with which their masses and orbital parameters are recovered.
