重新审视实时间隔和吞吐量最大化
Revisiting Real-Time Interval and Throughput Maximization
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中文总结 AI 辅助
研究实时模型中作业吞吐量最大化问题，探讨间隔调度结果对更一般吞吐量问题的扩展性，介绍新实时模型，给出不同情况下的竞争比及算法，如提前通知下无抢占的比例加权吞吐量常数竞争比等。
中文摘要 AI 辅助
作业吞吐量最大化是调度中的核心最大化问题。间隔调度是作业为间隔时吞吐量最大化的特殊情况，此时无松弛时间来调度作业。了解间隔调度的结果能在多大程度上扩展到实时模型中更一般的吞吐量问题很有趣。对于无加权和按比例加权的吞吐量问题，有使用抢占和重启的常数竞争实时调度算法。比例加权间隔调度的结果可扩展到C-仁慈权重函数。还引入了新实时模型，表明有足够提前通知时，可在无抢占情况下获得比例加权吞吐量的常数竞争比，但此结果不适用于任意C-仁慈和D-仁慈权重函数。最后表明，与间隔调度不同，当不同处理时间数量不受限时，使用撤销抢占的无加权吞吐量不存在常数竞争比，对于最多有k个不同处理时间的实例，给出了1/(k + 1)的下界和确定性的1/(2k)竞争算法。
英文摘要
Job throughput maximization is the central maximization problem in scheduling. Interval scheduling is the special case of throughput maximization when jobs are intervals and therefore there is no slack available in which to schedule a job. It is interesting to know to what extent results for interval scheduling can be extended to the more general throughput problem in the real-time model. For the unweighted and proportionally weighted throughput problem (where the weight or value $w_i$ of a job $J_i$ is its processing time $p_i$), there are constant competitive real-time scheduling algorithms using preemption with restarting. More generally, the result for proportionally weighted interval scheduling can be extended to C-Benevolent weight functions. We also introduce a new real-time model in which jobs are announced before the actual release time of a job. We show that with sufficient advance notice, we can obtain a constant competitive ratio for proportionally weighted throughput {\it without any preemption}. However, this advance notice result does not extend to arbitrary C-Benevolent and D-Benevolent weight functions. Finally, we show that unlike interval scheduling, unweighted throughput using preemption with revoking admits no constant competitive ratio when the number of distinct processing times is unrestricted. More precisely, for instances with at most $k$ distinct processing times, we give a lower bound of $1/(k+1)$ and a deterministic $1/(2k)$-competitive algorithm.
