The scheduling problem is a key class of optimization problems and has various kinds of applications both in practical and theoretical scenarios. In the scheduling problem, probabilistic analysis is a basic tool for investigating performance of scheduling algorithms, and therefore has been carried out by plenty amount of prior works. However, probabilistic analysis has several potential problems. For example, current research interest in the scheduling problem is limited to i.i.d. scenarios, due to its simplicity for analysis. This paper provides a new framework for probabilistic analysis in the scheduling problem and aims to deal with such problems. As a consequence, we obtain several theorems including a theoretical limit of the scheduling problem which can be applied to \emph{general, non-i.i.d. probability distributions}. Several information theoretic techniques, such as \emph{information-spectrum method}, turned out to be useful to prove our results. Since the scheduling problem has relations to many other research fields, our framework hopefully yields other interesting applications in the future.

翻译：调度问题是一类关键的优化问题，在理论和实际场景中均有多种应用。在调度问题中，概率分析是研究调度算法性能的基础工具，因此已有大量先前工作对此展开研究。然而，概率分析存在若干潜在问题。例如，当前调度问题的研究兴趣因分析简便性而局限于独立同分布（i.i.d.）场景。本文为调度问题的概率分析提供了新框架，旨在处理此类问题。作为研究结果，我们获得了若干定理，包括可应用于*一般非独立同分布（non-i.i.d.）概率分布*的调度问题理论极限。若干信息论技术（如*信息谱方法*）被证明对证明我们的结果有效。由于调度问题与许多其他研究领域相关，我们的框架有望在未来产生其他有趣的应用。