Scheduling Parallel Real-Time Tasks on the Minimum Number of Processors
Hyeonjoong Cho, Chul-Goo Kim, Joohyung Sun, Arvind Easwaran, Ju-Derk Park, Byeong-Cheol Choi · IEEE Transactions on Parallel and Distributed Systems · 2019
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 acapacity augmentation boundof 2. Our experimental results show that the proposed approach yields higher performance than one developed in a recent study.