Limited preemptive (LP) scheduling has been demonstrated to effectively improve the schedulability of fully preemptive (FP) and fully non-preemptive (FNP) paradigms. On one side, LP reduces the preemption related overheads of FP; on the other side, it restricts the blocking effects of FNP. However, LP has been applied to multi-core scenarios only when completely sequential task systems are considered. This paper extends the current state-of-the-art response time analysis for global fixed priority scheduling with fixed preemption points by deriving a new response time analysis for DAG-based task-sets.The research leading to these results is funded by the EU project PSOCRATES (FP7-ICT-2013-10) and the Spanish Ministry of Science and Innovatio...