急剧重启的尾部行为路线图
Tail-behavior roadmap for sharp restart
摘要：
许多任务是通过随机过程完成的。这样一个任务的完成时间可能会受到重启的深刻影响：偶尔重置任务的底层随机进程。因此，确定何时重启将阻碍或加速任务完成是一个非常重要的主题。近年来，研究者对这一问题进行了广泛的探索，主要关注的是平均行为，即平均完成时间。一方面，均值方法强调了“急剧重启”的中心性--使用确定性（固定）定时器进行重置。另一方面，均值方法的一个显著缺点是它没有提供关于尾部行为的洞察，即极端完成时间的发生可能性。针对急剧重启，并将重点从手段转移到极端，本文建立了一个全面的尾部行为分析的完成时间。采用可靠性工程的危险率的概念，分析产生了一组通用的结果，确定-从尾部行为的角度-当急剧重新启动将阻碍或加快任务完成。普遍的结果制定明确的和高度适用的危险率标准。利用这些新的结果，设计了一个通用的平均尾分类手册.该手册详细说明了一般情况下，急剧重启对平均行为和尾部行为产生相反的影响：减少平均完成时间，同时大大增加极端完成时间的可能性;相反，增加平均完成时间，同时大大减少极端完成时间的可能性。
英文摘要：
Many tasks are accomplished via random processes. The completion time of such a task can be profoundly affected by restart: the occasional resetting of the task's underlying random process. Consequently, determining when restart will impede or expedite task completion is a subject of major importance. In recent years researchers explored this subject extensively, with main focus set on average behavior, i.e. on mean completion times. On the one hand, the mean approach asserts the centrality of "sharp restart" -- resetting with deterministic (fixed) timers. On the other hand, a significant drawback of the mean approach is that it provides no insight regarding tail behavior, i.e. the occurrence likelihood of extreme completion times. Addressing sharp restart, and shifting the focus from means to extremes, this paper establishes a comprehensive tail-behavior analysis of completion times. Employing the reliability-engineering notion of hazard rate, the analysis yields a set of universal results that determine -- from a tail-behavior perspective -- when sharp restart will impede or expedite task completion. The universal results are formulated in terms of explicit and highly applicable hazard-rate criteria. With the novel results at hand, a universal average-&-tail classification manual for sharp restart is devised. The manual specifies general scenarios in which -- rather counter-intuitively -- sharp restart has an opposite effect on average behavior and on tail behavior: decreasing mean completion times while dramatically increasing the likelihood of extreme completion times; and, conversely, increasing mean completion times while dramatically decreasing the likelihood of extreme completion times.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
