Characterizations of Parallel Real-Time Workloads

Abstract

The work function, originally proposed by Bonifaci et al. [4], plays an important role in timing analysis of sporadic DAG parallel tasks. Later, Baruah [1] and Li et al. [10] provide different characterizations for Bonifaci’s notion of work function. The consistency and correctness of these characterizations and Bonifaci’s original result is so far a pending question. In this paper, we revisit the notion of work function based analysis techniques to answer the above pending question. We show that Baruah’s characterization is equivalent to Bonifaci’s original formulation, while Li’s characterization is strictly stronger.

The origins of this work can be traced back to 1986 when Wang, one of the authors, first met Jifeng at the Marktoberdorf Summer School on Theoretical Computer Science. The encounter marked the beginning of their professional collaboration and personal friendship, which has lasted for nearly four decades. During the school, Wang, a Ph.D. student at the time, got to know Jifeng’s work with Antony Hoare of algebraic theory on programming, which has deeply influenced on Wang’s subsequent research in process algebras, formal verification, and real-time computing. As one of the leading teams in the country in the field of embedded and real-time systems, the authors wish to take this opportunity to thank Jifeng for his unwavering support, inspiration, and friendship. Happy Birthday, Jifeng!.