Fixed priority scheduling is used in many real-time systems; however, both preemptive and non-preemptive variants (FP-P and FP-NP) are known to be sub-optimal when compared to an optimal uniprocessor scheduling algorithm such as preemptive earliest deadline first (EDF-P). In this paper, we investigate the sub-optimality of fixed priority non-preemptive scheduling. Specifically, we derive the exact processor speed-up factor required to guarantee the feasibility under FP-NP (i.e. schedulability assuming an optimal priority assignment) of any task set that is feasible under EDF-P. As a consequence of this work, we also derive a lower bound on the sub-optimality of non-preemptive EDF (EDF-NP). As this lower bound matches a recently published upper bound for the same quantity, it closes the exact sub-optimality for EDF-NP. It is known that neither preemptive, nor non-preemptive fixed priority scheduling dominates the other, in other words, there are task sets that are feasible on a processor of unit speed under FP-P that are not feasible under FP-NP and vice-versa. Hence comparing these two algorithms, there are non-trivial speedup factors in both directions. We derive the exact speed-up factor required to guarantee the FP-NP feasibility of any FP-P feasible task set. Further, we derive the exact speed-up factor required to guarantee FP-P feasibility of any constrained-deadline FP-NP feasible task set.

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非抢占式调度的精确加速因子和次优性

许多实时系统中使用固定优先级调度；然而，已知抢占式和非抢占式变体（FP-P 和 FP-NP）与最佳单处理器调度算法（例如抢占式最早期限优先（EDF-P））相比都是次优的。在本文中，我们研究了固定优先级非抢占式调度的次优性。具体来说，我们推导出准确的处理器加速因子，以保证在 EDF-P 下可行的任何任务集在 FP-NP 下的可行性（即假定最佳优先级分配的可调度性）。作为这项工作的结果，我们还推导出了非抢占式 EDF (EDF-NP) 的次优性的下限。由于此下限与最近发布的相同数量的上限相匹配，因此它关闭了 EDF-NP 的确切次优性。众所周知，无论是抢占式还是非抢占式固定优先级调度都占主导地位，换句话说，有任务集在 FP-P 下单位速度的处理器上可行，而在 FP-NP 下不可行，反之亦然。反之。因此，比较这两种算法，在两个方向上都有非平凡的加速因素。我们推导出保证任何 FP-P 可行任务集的 FP-NP 可行性所需的确切加速因子。此外，我们推导出了保证任何受约束的最后期限 FP-NP 可行任务集的 FP-P 可行性所需的确切加速因子。两个方向都有重要的加速因素。我们推导出保证任何 FP-P 可行任务集的 FP-NP 可行性所需的确切加速因子。此外，我们推导出了保证任何受约束的最后期限 FP-NP 可行任务集的 FP-P 可行性所需的确切加速因子。两个方向都有重要的加速因素。我们推导出保证任何 FP-P 可行任务集的 FP-NP 可行性所需的确切加速因子。此外，我们推导出了保证任何受约束的最后期限 FP-NP 可行任务集的 FP-P 可行性所需的确切加速因子。