###### Abstract  
With the rapid development of high-performance computing and parallel computing technology, by virtue of its cost-effectiveness, strong scalability, and easy programming, the multiprocessor system has gradually become the mainstream computing platform. Meanwhile, a growing number of researchers pay attention to the performance of multiprocessor systems, especially the task scheduling problem, which has an important impact on the system performance. Most of the current research works on task scheduling algorithms are based on the homogeneous computing environment. On the contrary, research works focusing on more complex performance asymmetric multiprocessor environments still remain rare. In this paper, we compare the effects of three earliest deadline first algorithms under different processor allocation strategies on performance asymmetric multiprocessors. We propose an efficient schedulability analysis for an allocation strategy that assigns high-priority tasks to the slowest idle processor. Experimental results show that the strategy of allocating processors with optimum speeds for high-priority tasks can schedule more task sets than the other two allocation strategies. The strategy that prioritizes the slowest processors for high-priority tasks has the smallest number of task migrations, and the strategy has the highest effective processor utilization. EDF scheduling algorithm; performance asymmetric multiprocessors; schedulability analysis +
Footnote †: journal: Applied  
performance asymmetric multiprocessors cannot make full use of the performance in the real-time system [5]. To track this challenge, researchers have proposed some works. The earliest deadline first (EDF) scheduling algorithm was proposed by [PERSON] et al. [6]. It is optimal on a single processor. EDF's computable schedulability test was demonstrated by [PERSON] et al. on homogeneous multiprocessors [7]. On symmetric multiprocessors, an algorithm that improves the schedulability of non-preemptive tasks was proposed by [PERSON] et al. [8]. For the global EDF, [PERSON] et al. obtained a more accurate response time analysis method [9]. [PERSON] et al. improved the schedulability of the DAG task system [10]. Their new approach combines federated scheduling and global EDF. Now, the field of unmanned vehicle research is very popular, and many large companies have also invested a lot of energy in the research of unmanned vehicles. The Linux kernel is used in many companies' unmanned vehicle operating systems, such as Tesla's operating system. The scheduling strategy of the Linux kernel has used scheduling algorithms such as Completely Fair Scheduling (CFS) and EDF. Thus, the study of EDF is very important. The processor allocation strategy used in previous EDF scheduling algorithms studies on performance asymmetric multiprocessors aims to assign the high-priority tasks to the fastest processors. However, few researchers take the allocation of processors into consideration. To address this issue, we believe that it is possible to assign the high-priority tasks to a suitable or slow-speed processor. In this paper, we study the different processor allocation strategies of EDF in performance asymmetric multiprocessor platforms. The EDF scheduling algorithm assigns priority according to the deadline of the task, and assigns the processor according to the priority. The fastest speed fit earliest deadline first (FSF-EDF) scheduling algorithm assigns high-priority tasks to the fastest processors. The best speed fit earliest deadline first (BSF-EDF) scheduling algorithm seeks to assign high-priority tasks to the most suitable speed processor. The slowest speed fit earliest deadline first (SSF-EDF) scheduling algorithm seeks to assign high-priority tasks to the slowest speed processor first. Thus, we propose a schedulability test for SSF-EDF. Below are the main contributions of this paper.