  The online feasibility problem (for a set of sporadic tasks) asks whether
there is a scheduler that always prevents deadline misses (if any), whatever
the sequence of job releases, which is a priori} unknown to the scheduler. In
the multiprocessor setting, this problem is notoriously difficult. The only
exact test for this problem has been proposed by Bonifaci and
Marchetti-Spaccamela: it consists in modelling all the possible behaviours of
the scheduler and of the tasks as a graph; and to interpret this graph as a
game between the tasks and the scheduler, which are seen as antagonistic
players. Then, computing a correct scheduler is equivalent to finding a winning
strategy for the `scheduler player', whose objective in the game is to avoid
deadline misses. In practice, however this approach is limited by the
intractable size of the graph. In this work, we consider the classical
attractor algorithm to solve such games, and introduce antichain techniques to
optimise its performance in practice and overcome the huge size of the game
graph. These techniques are inspired from results from the formal methods
community, and exploit the specific structure of the feasibility problem. We
demonstrate empirically that our approach allows to dramatically improve the
performance of the game solving algorithm.
