The delay composition theorem on pipeline systems with non-preemptive priority varying scheduling algorithms

The delay composition theorem, by taking into account the fact that pipeline systems allow concurrent execution, expresses the upper-bounded delay of a real-time task as the sum of two summations, where the first one is linear to the number of stages of the system, and the second one is linear to the number of tasks running on the system. The schedulability analysis based on delay composition theorem performs better than traditional analysis techniques. In this paper we break one assumption that has been hold by previous works on delay composition theorem, namely each task has the same relative priority across all stages. We extend the theorem to pipeline systems running non-preemptive scheduling algorithm which may assign different relative priorities to a task on different stages