Response Time Analysis for Prioritized DAG Task with Mutually Exclusive Vertices

Directed acyclic graph (DAG) becomes a popular model for modern real-time embedded software. It is really a challenge to bound the worst-case response time (WCRT) of DAG task. Parallelism, dependencies and mutual exclusion become three of the most critical properties of real-time parallel tasks. Recent work applied prioritizing techniques to reduce DAG task's WCRT bound, which has well studied the first two properties, i.e., parallelism and dependencies, but leaves the mutually exclusive property as an open problem. This paper focuses on all the three properties of real-time parallel software, and investigates how to estimate the WCRT of the DAG task model with mutually exclusive vertices and under prioritized list scheduling algorithms. We derive a reasonable WCRT bound for such a complicated DAG task, and prove that the corresponding WCRT bound computation problem is strongly NP-hard. It means that there are no pseudo-polynomial time algorithms to compute the WCRT bound. For the prioritized DAG with a constant number of mutual exclusive vertices, we develop a dynamic programming algorithm that is able to estimate the WCRT bound within pseudo-polynomial time. Experiments are conducted to evaluate the performance of our analysis method implemented with different priority assignment policies against the state-of-the-art.