Federated Scheduling Admits No Constant Speedup Factors for Constrained-Deadline DAG Task System

In the federated scheduling approaches in multiprocessor systems, a task (1) either is restricted for sequential executions or (2) has exclusive access to the assigned processors. There have been several positive results to conduct good federated scheduling policies, with a constant speedup factor with respect to the optimal federated scheduling. This paper answers an open question: "For constrained-deadline task systems, is federated scheduling a good strategy, compared to the optimal schedules?" The answer is "No!". This paper presents an example, which demonstrates that an optimal federated schedule in multiprocessor scheduling has a speedup factor at least $\Omega(\min\{M, N\})$, where $N$ is the number of the given tasks and $M$ is the number of the given processors.