多处理器系统上的零星实时的任务打包
Packing Sporadic Real-Time Tasks on Identical Multiprocessor Systems
摘要：
在实时的【形】系统中，除了功能正确性外，循环任务还必须满足时间约束，以确保系统的正确行为。分区调度广泛应用于实时的【形】系统中，即，任务被静态地分配到处理器上，同时确保满足所有定时约束。决策版本的问题，这是检查是否可以满足任务的最后期限约束在一个给定的相同的处理器数量，已被称为${\cal NP}$ -完全的强意义。关于这个问题的几项研究是基于涉及资源增加的近似，即，加速单个处理器。本文研究了另一种类型的资源增加分配额外的处理器，一个主题，直到最近才被探索。我们提供多项式时间算法和分析，其中的近似因子取决于输入实例。具体而言，这些因素与给定任务集中任务的周期与相对截止日期的最大比率有关。我们还表明，不幸的是，这些算法不能实现一个常数的近似因子一般情况下。此外，我们证明了该问题不允许任何渐近多项式时间近似方案（APTAS），除非${\cal P}={\cal NP}$时，任务集有约束的最后期限，即，任务的相对截止期不超过任务的周期。
英文摘要：
In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are statically assigned onto processors while ensuring that all timing constraints are met. The decision version of the problem, which is to check whether the deadline constraints of tasks can be satisfied on a given number of identical processors, has been known ${\cal NP}$-complete in the strong sense. Several studies on this problem are based on approximations involving resource augmentation, i.e., speeding up individual processors. This paper studies another type of resource augmentation by allocating additional processors, a topic that has not been explored until recently. We provide polynomial-time algorithms and analysis, in which the approximation factors are dependent upon the input instances. Specifically, the factors are related to the maximum ratio of the period to the relative deadline of a task in the given task set. We also show that these algorithms unfortunately cannot achieve a constant approximation factor for general cases. Furthermore, we prove that the problem does not admit any asymptotic polynomial-time approximation scheme (APTAS) unless ${\cal P}={\cal NP}$ when the task set has constrained deadlines, i.e., the relative deadline of a task is no more than the period of the task.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
