Real-time embedded systems are increasingly being implemented on heterogeneous multiprocessor platforms in which the same piece of software may require different amounts of time to execute on different processors. Computation of optimal schedules for such systems is non-trivial. Recently, Zhang et al. proposed linear and dynamic programming algorithms for real-time task scheduling for heterogeneous platforms. The authors have formulated a linear programming problem which is then iteratively solved by the linear programming algorithm (LPA) to produce a feasible schedule. Further, they compared the performance of LPA against their proposed dynamic programming algorithm (DPA) and claimed that LPA is superior to DPA, in terms of scalability. In this paper, we show that their linear programming problem does not correctly capture the execution requirement of real-time tasks on heterogeneous platforms . Consequently, LPA fails to produce valid execution schedules for most task sets presented to it. We first illustrate this flaw and strengthen our claim theoretically using a counterexample. Then, we present necessary modifications to their linear programming formulation to address the identified flaw. Finally, we show that our proposed algorithm can be used to find a feasible schedule for real-time task sets, using a real-world case study and experiments.

中文翻译：

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解决在异构平台上捕获执行需求的缺点

实时嵌入式系统越来越多地在异构多处理器平台上实现，其中同一个软件可能需要不同的时间在不同的处理器上执行。计算此类系统的最佳调度是非常重要的。最近，张等人。提出了用于异构平台实时任务调度的线性和动态规划算法。作者制定了一个线性规划问题，然后通过线性规划算法 (LPA) 迭代解决该问题以生成可行的计划。此外，他们将 LPA 的性能与他们提出的动态编程算法 (DPA) 进行了比较，并声称 LPA 在可扩展性方面优于 DPA。在本文中，我们表明他们的线性规划问题没有正确捕捉异构平台上实时任务的执行要求。因此，LPA 无法为提交给它的大多数任务集生成有效的执行计划。我们首先说明这个缺陷，并使用反例从理论上加强我们的主张。然后，我们对其线性规划公式进行必要的修改，以解决已识别的缺陷。最后，我们展示了我们提出的算法可用于通过实际案例研究和实验为实时任务集找到可行的时间表。我们对他们的线性规划公式进行了必要的修改，以解决已识别的缺陷。最后，我们展示了我们提出的算法可用于通过实际案例研究和实验为实时任务集找到可行的时间表。我们对他们的线性规划公式进行了必要的修改，以解决已识别的缺陷。最后，我们展示了我们提出的算法可用于通过实际案例研究和实验为实时任务集找到可行的时间表。