可调度测试的时间可逆性

Jinkyu Lee
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引用次数: 11

摘要

为了保证一组实时任务在目标调度算法下的定时性,研究了一系列可调度性测试。然而,仍然存在许多任务集,它们可能被目标调度算法调度,但没有任何现有的可调度性测试证明是可调度的,特别是在多处理器平台上。本文提出了可调度性测试的时间可逆性的新概念,通过观察时间符号变化下的实时调度,可以得到更严格的可调度性保证。为此,我们首先定义了针对目标调度算法的时间反转调度算法的概念,例如,针对EDF(最早的截止日期优先)的时间反转调度算法是LCFS(最后来的,先服务的),反之亦然。然后,对于调度算法的可调度性测试,如果测试认为可调度的所有任务集也可以通过其时间反转调度算法进行调度,则该可调度性测试就可调度性而言是时间可逆的。为了利用时间可逆性的概念来实现更严格的可调度性保证,我们不仅证明了现有可调度性测试的时间可逆性,而且开发了一个新的时间可逆性测试,这两个测试都涵盖了额外的可调度任务集。其次,我们将时间可逆性理论推广到部分执行。利用这一概念,我们可以通过分而治之的方式来保证目标调度算法下任务的可调度性:(i)调度算法的可调度性测试保证前几个执行单元的可调度性,(ii)时间反转调度算法的时间可逆(相对于部分执行)可调度性测试保证剩余执行单元的可调度性。这种分而治之的方法没有直接应用于现有的可调度性测试,因为它们不能有效地解决(二)问题。作为案例研究,本文开发了lfs的RTA(响应时间分析),证明了其时间可逆性,并将分而治之的方法与现有的EDF可调度性测试一起应用于测试。我们的仿真结果表明,时间可逆性理论有助于在多处理器平台上找到高达13.1%的额外edf可调度任务集。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Time-Reversibility of Schedulability Tests
For timing guarantees of a set of real-time tasks under a target scheduling algorithm, a number of schedulability tests have been studied. However, there still exist many task sets that are potentially schedulable by a target scheduling algorithm, but proven schedulable by none of existing schedulability tests, especially on a multiprocessor platform. In this paper, we propose a new notion of time-reversibility of schedulability tests, which yields tighter schedulability guarantees by viewing real-time scheduling under a change in the sign of time. To this end, we first define the notion of a time-reversed scheduling algorithm against a target scheduling algorithm, for example, the time-reversed scheduling algorithm against EDF (Earliest Deadline First) is LCFS (Last-Come, First-Served), and the converse also holds. Then, a schedulability test for a scheduling algorithm is said to be time-reversible with respect to schedulability, if all task sets deemed schedulable by the test are also schedulable by its time-reversed scheduling algorithm. To exploit the notion of time-reversibility for tighter schedulability guarantees, we not only prove time-reversibility of an existing schedulability test, but also develop a new time-reversible schedulability test, both of which cover additional schedulable task sets. Next, we generalize the time-reversibility theory towards partial execution. Utilizing the notion, we can assure the schedulability of a task under a target scheduling algorithm in a divide-and-conquer manner: (i) the first some units of execution guaranteed by a schedulability test for the scheduling algorithm, and (ii) the remaining execution guaranteed by a time-reversible (with respect to partial execution) schedulability test for its time-reversed scheduling algorithm. Such a divide-and-conquer approach has not been directly applied to existing schedulability tests in that they cannot address (ii) effectively. As a case study, this paper develops RTA (Response-Time Analysis) for LCFS, proves its time-reversibility, and applies the divide-and-conquer approach to the test along with an existing EDF schedulability test. Our simulation results show that the time-reversibility theory helps to find up to 13.1% additional EDF-schedulable task sets on a multiprocessor platform.
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