Fixed-point iteration algorithms like RTA (response time analysis) and QPA (quick processor-demand analysis) are arguably the most popular ways of solving schedulability problems for preemptive uniprocessor FP (fixed-priority) and EDF (earliest-deadline-first) systems. Several IP (integer program) formulations have also been proposed for these problems but it is unclear whether the algorithms for solving these formulations are related to RTA and QPA. By discovering connections between the problems and the algorithms, we show that RTA and QPA are, in fact, suboptimal cutting-plane algorithms for specific IP formulations of FP and EDF schedulability. We propose optimal cutting-plane algorithms for these IP formulations; clearly, these new schedulability tests have better convergence rates than RTA and QPA. We compare the new tests with RTA and QPA on large collections of synthetic task sets to gauge the improvement in convergence rates.

翻译：像RTA（响应时间分析）和QPA（快速处理器需求分析）这样的定点迭代算法，可以说是解决抢占式单处理器FP（固定优先级）和EDF（最早截止时间优先）系统可调度性问题最常用的方法。针对这些问题，也有几种IP（整数规划）公式被提出，但求解这些公式的算法是否与RTA和QPA相关尚不清楚。通过发现这些问题与算法之间的联系，我们证明RTA和QPA实际上分别是FP和EDF可调度性特定IP公式的次优切割平面算法。我们为这些IP公式提出了最优切割平面算法；显然，这些新的可调度性测试比RTA和QPA具有更优的收敛速度。我们在大量合成任务集上将新测试与RTA和QPA进行了比较，以评估收敛速度的改进程度。