This paper presents a new strategy to arbitrate the access to globally shared resources in hierarchical EDF sched-uled real-time systems, without needing any information on the duration of each critical section. Previous works addressing this problem assumed each task worst-case critical section length be known in advance. However, this assumption is valid only in restricted system domains, and is definitely inadequate for general purpose real-time operating systems. To sidestep this problem, we will in-stead measure at run-time the amount of time for which a task keeps a resource locked, assuring that there is enough bandwidth to tolerate the interferences associated to such measured blocking times. The protocol will execute each critical ...