OpenMP offers a tasking model very convenient to develop critical real-time parallel applications by virtue of its time predictability. However, current implementations make an intensive use of dynamic memory to efficiently manage the parallel execution. This jeopardizes the qualification process and limits the use of OpenMP in architectures with limited amount of memory. This work introduces an OpenMP framework that statically allocates the data structures needed to efficiently manage parallel execution in OpenMP programs. We achieve the same performance than current implementations, while bounding and reducing the dynamic memory requirements at runtime.