As multicore processors become ever more prevalent, it is important for real-time programs to take advantage of intra-task parallelism in order to support computation-intensive applications with tight deadlines. We prove that a Global Earliest Deadline First (GEDF) scheduling policy provides a capacity augmentation bound of 4-2/m and a resource augmentation bound of 2-1/m for parallel tasks in the general directed a cyclic graph model. For the proposed capacity augmentation bound of 4-2/m for implicit deadline tasks under GEDF, we prove that if a task set has a total utilization of at most m/(4-2/m) and each task's critical path length is no more than 1/(4-2/m) of its deadline, it can be scheduled on a machine with m processors under GEDF. Our capacity augmentation bound therefore can be used as a straightforward schedulability test. For the standard resource augmentation bound of 2-1/m for arbitrary deadline tasks under GEDF, we prove that if an ideal optimal scheduler can schedule a task set on m unit-speed processors, then GEDF can schedule the same task set on m processors of speed 2-1/m. However, this bound does not lead to a schedulabilty test since the ideal optimal scheduler is only hypothetical and is not known. Simulations confirm that the GEDF is not only safe under the capacity augmentation bound for various randomly generated task sets, but also performs surprisingly well and usually outperforms an existing scheduling technique that involves task decomposition.