  We consider a task graph mapped on a set of homogeneous processors. We aim at
minimizing the energy consumption while enforcing two constraints: a prescribed
bound on the execution time (or makespan), and a reliability threshold. Dynamic
voltage and frequency scaling (DVFS) is an approach frequently used to reduce
the energy consumption of a schedule, but slowing down the execution of a task
to save energy is decreasing the reliability of the execution. In this work, to
improve the reliability of a schedule while reducing the energy consumption, we
allow for the re-execution of some tasks. We assess the complexity of the
tri-criteria scheduling problem (makespan, reliability, energy) of deciding
which task to re-execute, and at which speed each execution of a task should be
done, with two different speed models: either processors can have arbitrary
speeds (continuous model), or a processor can run at a finite number of
different speeds and change its speed during a computation (VDD model). We
propose several novel tri-criteria scheduling heuristics under the continuous
speed model, and we evaluate them through a set of simulations. The two best
heuristics turn out to be very efficient and complementary.
