Abstract In stochastic online scheduling problems, a common class of policies is the class of fixed assignment policies. These policies first assign jobs to machines and then apply single machine scheduling policies for each machine separately. We consider a stochastic online scheduling problem for which the goal is to minimize total weighted expected completion time on uniform parallel machines. To solve the problem, we adapt policies introduced for the identical and unrelated parallel machine environments. We show that, with the help of lower bounds specific for the uniform machine environment, we can tighten the performance guarantees that are implied by the results for the unrelated machine environment for the special case of two machine speeds. Furthermore, in the Online-List model we show that a greedy assignment policy is asymptotically optimal. Finally, we construct a computational study to assess the performance of the policies in practice.

中文翻译：

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均匀并行机随机在线调度固定分配策略的性能分析

摘要 在随机在线调度问题中，一类常见的策略是固定分配策略类。这些策略首先将作业分配给机器，然后分别为每台机器应用单机调度策略。我们考虑一个随机在线调度问题，其目标是最小化统一并行机器上的总加权预期完成时间。为了解决这个问题，我们调整了为相同和不相关的并行机环境引入的策略。我们表明，在特定于统一机器环境的下界的帮助下，我们可以加强对两种机器速度的特殊情况下无关机器环境的结果所暗示的性能保证。此外，在在线列表模型中，我们表明贪婪分配策略是渐近最优的。最后，我们构建了一个计算研究来评估政策在实践中的表现。