Response time analysis of digraph real-time tasks scheduled with static priority: generalization, approximation, and improvement

Abstract

Graph-based task models have been studied to better model and analyze the schedulability of real-time systems. Among them, the digraph task model, with its powerful expressiveness to describe the behavior of a large class of real-time tasks, receives a wide range of interests recently. However, the exact schedulability analysis of digraph tasks on a uni-processor with preemptive static-priority scheduling has been shown to be coNP-hard. Approximate analyses based on the request and interference bound functions ($\textit{rbf}$ and $\textit{ibf}$) have been proposed to improve the analysis efficiency. In this work, we summarize the existing results on these analysis techniques, and seek to further improve their generality, complexity, and accuracy. Specifically, we develop analysis techniques for tasks with arbitrary deadlines. We prove the periodicity of interference bound function such that it can be expressed as a finite aperiodic part and an infinite periodic part, which makes the asymptotic complexity of its calculation independent from the length of the time interval. Moreover, we develop a linear upper bound on $\textit{ibf}$ that is tighter than that of $\textit{rbf}$, to derive a better response time bound.