  To satisfy the increasing performance needs of modern cyber-physical systems,
multiprocessor architectures are increasingly utilized. To efficiently exploit
their potential parallelism in hard real-time systems, appropriate task models
and scheduling algorithms that allow providing timing guarantees are required.
Such scheduling algorithms and the corresponding worst-case response time
analyses usually suffer from resource over-provisioning due to pessimistic
analyses based on worst-case assumptions. Hence, scheduling algorithms and
analysis with high resource efficiency are required. A prominent parallel task
model is the directed-acyclic-graph (DAG) task model, where precedence
constrained subjobs express parallelism.
  This paper studies the real-time scheduling problem of sporadic
arbitrary-deadline DAG tasks. We propose a path parallel progression scheduling
property with only two distinct subtask priorities, which allows to track the
execution of a collection of paths simultaneously. This novel approach
significantly improves the state-of-the-art response time analyses for parallel
DAG tasks for highly parallel DAG structures. Two hierarchical scheduling
algorithms are designed based on this property, extending the parallel path
progression properties and improving the response time analysis for sporadic
arbitrary-deadline DAG task sets.
