# A Comparative Study on the Schedulability of the EDZL Scheduling Algorithm on Multiprocessors
## 1 Introduction
The demand-based test outperforms other EDZL schedulability tests in terms of the number of admitted task sets. They also showed that the demand-based test is not dominated by other tests. The above research evaluated the EDZL schedulability tests from a quantitative perspective. The EDZL schedulability tests are compared in terms of the number of admitted task sets. But, these tests are not fully evaluated from a qualitative perspective. Whether the demand-based test dominates other tests is not revealed. The dominance between [PERSON]'s test and other tests is not disclosed, either. On the other hand, the EDZL schedulability tests have not been compared with other scheduling algorithms' schedulability tests, which are also practical and have comparable performance. This paper evaluates the schedulability of the EDZL algorithm. First, we compare the performance of the EDZL schedulability tests from a quantitative and qualitative perspective. We generate all possible task sets in a restricted range and analyze them with the above-mentioned schedulability tests. We measure and compare the ratio of task sets admitted by each test. As a result, the demand-based schedulability test outperforms other tests, similarly to the experimental results in reference [20]. We also investigate the dominance between the EDZL schedulability tests. We prove that the utilization-based test dominates [PERSON]'s test. And we discover that the slack-based test, the utilization-based test and the demand-based test do not dominate each other. The experimental results implies that the union of the demand-based test and the utilization-based test is an effective combination. Second, we compare the schedulability of EDZL with \(\text{EDF}^{(k)}\)[21], which is another practical multiprocessor real-time scheduling algorithm. We find out that the utilization-based EDZL schedulability test is equivalent to the \(\text{EDF}^{(k)}\) schedulability test. This implies that the union of the EDZL schedulability tests dominates the \(\text{EDF}^{(k)}\) schedulability test, i.e., the EDZL schedulability test can admit all task sets admitted by the \(\text{EDF}^{(k)}\) schedulability test. We also compare the schedulability of EDZL and \(\text{EDF}^{(k)}\) through scheduling simulation. We measure and compare the ratio of successfully scheduled task sets. EDZL can successfully schedule 7.0% more instances than \(\text{EDF}^{(k)}\). The contributions of this work are as follows. * The dominance between the EDZL schedulability tests is unveiled. The utilization-based test dominates [PERSON]'s test. The slack-based, utilization-based, and demand-based tests do not dominate each other. * This work proves that the utilization-based EDZL schedulability test is equivalent to the \(\text{EDF}^{(k)}\) schedulability test. The two tests dominate each other. * A EDZL schedulability test that dominates the EDF\({}^{(k)}\) schedulability test can be easily constructed by unioning the EDZL schedulability tests. The union of the EDZL schedulability tests admits more task sets than the EDF\({}^{(k)}\) schedulability test. * The performance of EDZL and EDF\({}^{(k)}\) scheduling was compared in terms of the number of successfully scheduled task sets. We found out that EDZL can accommodate more task sets than EDF\({}^{(k)}\). This paper is organized as follows. Section 2 provides the background knowledge about the EDZL and EDF\({}^{(k)}\) schedulability tests. Section 3 compares the performance of the EDZL schedulability tests. Section 4 compares the performance of EDZL and EDF\({}^{(k)}\) scheduling. Finally, Section 5 concludes our work.