Multipath Bound for DAG Tasks

This article studies the response time bound of a directed acyclic graph (DAG) task. Recently, the idea of using multiple paths to bound the response time of a DAG task, instead of using a single longest path in previous results, was proposed and led to the so-called multipath bound. Multipath bounds can greatly reduce the response time bound and significantly improve the schedulability of DAG tasks. This article derives a new multipath bound and proposes an optimal algorithm to compute this bound. We further present a systematic analysis on the dominance and the sustainability of three existing multipath bounds and the proposed multipath bound. Our bound theoretically dominates and empirically outperforms all existing multipath bounds. What is more, the proposed bound is the only multipath bound that is proved to be self-sustainable.