This paper studies an optimal ON-OFF control problem for a class of discrete event systems with real-time constraints. Our goal is to minimize the overall costs, including the operating cost and the wake-up cost, while still guaranteeing the deadline of each individual task. In particular, we consider the homogeneous case in which it takes the same amount of time to serve each task and each task needs to be served by d seconds upon arrival. The problem involves two subproblems: (i) finding the best time to wake up the system and (ii) finding the best time to let the system go to sleep. We study the two subproblems in both off-line and on-line settings. In the off-line case that all task information is known a priori, we combine sample path analysis and dynamic programming to come up with the optimal solution. In the on-line scenario where future task information is completely unknown, we show that the optimal time to wake up the system can be obtained without relying on future task arrivals. We also perform competitive analysis for on-line control and derive the competitive ratios for both deterministic and random controllers.

中文翻译：

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一类具有实时约束的离散事件系统的最优开关控制

本文研究了一类具有实时约束的离散事件系统的最优开-关控制问题。我们的目标是最大限度地降低总体成本，包括运营成本和唤醒成本，同时仍然保证每个单独任务的截止日期。特别地，我们考虑了同构情况，其中为每个任务提供相同的时间，并且每个任务需要在到达后 d 秒内得到服务。该问题涉及两个子问题：（i）找到唤醒系统的最佳时间和（ii）找到让系统进入睡眠状态的最佳时间。我们在离线和在线设置中研究这两个子问题。在所有任务信息都是先验已知的离线情况下，我们结合样本路径分析和动态规划来提出最佳解决方案。在未来任务信息完全未知的在线场景中，我们表明可以在不依赖未来任务到达的情况下获得唤醒系统的最佳时间。我们还对在线控制进行竞争分析，并推导出确定性和随机控制器的竞争比率。