In this paper, we consider four semi-online early work maximization problems on two hierarchical uniform machines \(M_1\) and \(M_2\), where machine \(M_1\) with speed \(s>0\) is available for all jobs and machine \(M_2\) with speed 1 is only available for high-hierarchy jobs. When the total size of all jobs is known, we design an optimal online algorithm with a competitive ratio of \(\min \{1+s,\frac{2+2s}{1+2s}\}\). When the total size of low-hierarchy jobs is known, we design an optimal online algorithm with a competitive ratio of \(\min {\{1+s, \frac{\sqrt{9\,s^2+10\,s+1}-s-1}{2\,s}}\}\). When the total size of high-hierarchy jobs is known, we design an optimal online algorithm with a competitive ratio of \(\min \{\sqrt{s+1}, \sqrt{s^2+2\,s+2}-s\}\). When both the total sizes of low-hierarchy and high-hierarchy jobs are known, we give a lower bound \(\frac{2s+2}{s+2}\) for the case \(s\le \frac{2}{3}\), and an optimal online algorithm with a competitive ratio of \(\frac{3s+3}{3s+2}\) for the case \(s>\frac{2}{3}\).

在本文中，我们考虑两个分层统一机器\(M_1\)和\(M_2\)上的四个半在线早期工作最大化问题，其中速度\(s>0\)的机器\(M_1\)可用于所有作业和速度为 1 的机器\(M_2\)仅适用于高层次作业。当所有作业的总规模已知时，我们设计一个竞争比为\(\min \{1+s,\frac{2+2s}{1+2s}\}\) 的最佳在线算法。当低层次作业的总规模已知时，我们设计一个最佳在线算法，其竞争比为\(\min {\{1+s, \frac{\sqrt{9\,s^2+10\, s+1}-s-1}{2\,s}}\}\)。当高层次作业的总规模已知时，我们设计一个最佳在线算法，其竞争比为\(\min \{\sqrt{s+1}, \sqrt{s^2+2\,s+2 }-s\}\)。当低层次结构和高层次结构作业的总大小已知时，我们给出情况\(s\le \frac{2} 的下界 \ (\frac{2s+2}{s+2}\) }{3}\) ，以及针对\(s>\frac{2}{3}\)情况竞争比为\(\frac{3s+3}{3s+2}\) 的最优在线算法。