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, where optimality is defined with respect to convergence rate. We propose optimal cutting-plane algorithms for these IP formulations. We compare the new algorithms with RTA and QPA on large collections of synthetic systems to gauge the improvement in convergence rates and running times.

翻译：固定点迭代算法，如RTA（响应时间分析）和QPA（快速处理器需求分析），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流行的方法。针对这些问题，已有多个IP（整数规划）模型被提出，但求解这些模型的算法是否与RTA和QPA相关尚不明确。通过揭示问题与算法之间的关联，我们证明RTA和QPA实际上是FP和EDF可调度性特定IP模型的次优割平面算法，其中最优性由收敛速率定义。我们针对这些IP模型提出了最优割平面算法，并在大量合成系统上将新算法与RTA和QPA进行了比较，以评估收敛速率和运行时间的改进。