Multiprocessor hardware platforms are now being considered for embedded systems, due to their high computational power and little additional cost when compared to single processor systems. When scheduling real-time applications on multiprocessor platforms, a possibility is to use global scheduling, where a scheduling algorithm dynamically assign tasks to processors, and tasks can migrate from one processor to another during their execution. In this paper, we tackle the problem of schedulability analysis of sporadic tasks in global scheduling systems, where the scheduler is the Earliest Deadline First (EDF) algorithm. We provide two main contributions. First, we show that two recently proposed tests perform poorly when the task set contains heavy tasks (i.e. tasks with high utilization). We also show that neither test dominates the other. As a second contribution, we introduce a new schedulability test that improves significantly the percentage of accepted task sets, especially when considering task sets containing heavy tasks. We show the effectiveness of the proposed test through an extensive set of experiments.