Scheduling Parallel Real-Time Tasks on the Minimum Number of Processors

• Published in: IEEE transactions on parallel and distributed systems Vol. 31; no. 1; pp. 171 - 186
• Main Authors: Cho, Hyeonjoong, Kim, Chulgoo, Sun, Joohyung, Easwaran, Arvind, Park, Ju-Derk, Choi, Byeong-Cheol
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Computational modeling; flow networks; Job shops; linear programming; maximum flow problem; minimum cost flow problem; Multicore processing; multicores; multiprocessors; Optimization; Polynomials; Precedence constraints; Processor scheduling; Processors; Production scheduling; Program processors; Real time; Real-time scheduling; Real-time systems; Scheduling; Task analysis; Task scheduling
• ISSN: 1045-9219; 1558-2183
• DOI: 10.1109/TPDS.2019.2929048

Recently, several parallel frameworks have emerged to utilize the increasing computational capacity of multiprocessors. Parallel tasks are distinguished from traditional sequential tasks in that the subtasks contained in a single parallel task can simultaneously execute on multiple processors. In this study, we consider the scheduling problem of minimizing the number of processors on which the parallel real-time tasks feasibly run. In particular, we focus on scheduling sporadic parallel real-time tasks, in which precedence constraints between subtasks of each parallel task are expressed using a directed acyclic graph (DAG). To address the problem, we formulate an optimization problem that aims to minimize the maximum processing capacity for executing the given tasks. We then suggest a polynomial solution consisting of three steps: (1) transform each parallel real-time task into a series of multithreaded segments, while respecting the precedence constraints of the DAG; (2) selectively extend the segment lengths; and (3) interpret the problem as a flow network to balance the flows on the terminal edges. We also provide the schedulability bound of the proposed solution: it has a capacity augmentation bound of 2. Our experimental results show that the proposed approach yields higher performance than one developed in a recent study.