We study single-machine scheduling of jobs, each belonging to a job type that determines its duration distribution. We start by analyzing the scenario where the type characteristics are known and then move to two learning scenarios where the types are unknown: non-preemptive problems, where each started job must be completed before moving to another job; and preemptive problems, where job execution can be paused in the favor of moving to a different job. In both cases, we design algorithms that achieve sublinear excess cost, compared to the performance with known types, and prove lower bounds for the non-preemptive case. Notably, we demonstrate, both theoretically and through simulations, how preemptive algorithms can greatly outperform non-preemptive ones when the durations of different job types are far from one another, a phenomenon that does not occur when the type durations are known.

翻译：我们研究单机作业调度问题，每个作业属于决定其持续时间分布的作业类型。首先分析类型特征已知的场景，随后转向两种类型未知的学习场景：非抢占式问题（每个已启动的作业必须在切换到其他作业前完成）和抢占式问题（可暂停当前作业以执行其他作业）。针对这两种情况，我们设计了与已知类型性能相比具有次线性超额成本的算法，并证明了非抢占式情况下的下界。值得注意的是，我们通过理论和仿真证明：当不同类型作业的持续时间差异较大时（这在类型持续时间已知时不会发生），抢占式算法能显著优于非抢占式算法。