  Simple, controllable models play an important role to learn how to manipulate
and control quantum resources. We focus here on quantum non-Markovianity and
model the evolution of open quantum systems by quantum renewal processes. This
class of quantum dynamics provides us with a phenomenological approach to
characterise dynamics with a variety of non-Markovian behaviours, here
described in terms of the trace distance between two reduced states. By
adopting a trajectory picture for the open quantum system evolution, we analyse
how non-Markovianity is influenced by the constituents defining the quantum
renewal process, namely the time-continuous part of the dynamics, the type of
jumps and the waiting time distributions. We focus not only on the mere value
of the non-Markovianity measure, but also on how different features of the
trace distance evolution are altered, including times and number of revivals.
