  In the federated scheduling approaches in multiprocessor systems, a task
either 1) is restricted to execute sequentially on a single processor or 2) has
exclusive access to the assigned processors. There have been several positive
results to conduct good federated scheduling policies, which have constant
speedup factors with respect to any optimal federated scheduling algorithm.
This paper answers an open question: "For constrained-deadline task systems
with directed acyclic graph (DAG) dependency structures, do federated
scheduling policies have a constant speedup factor with respect to any optimal
scheduling algorithm?" The answer is "No!" This paper presents an example,
which demonstrates that any federated scheduling algorithm has a speedup factor
of at least $\Omega(\min\{M, N\})$ with respect to any optimal scheduling
algorithm, where $N$ is the number of tasks and $M$ is the number of
processors.
