Ultra-reliable low-latency communication (URLLC) constitutes a key service class of the fifth generation and beyond cellular networks. Notably, designing and supporting URLLC poses a herculean task due to the fundamental need to identify and accurately characterize the underlying statistical models in which the system operates, e.g., interference statistics, channel conditions, and the behavior of protocols. In general, multi-layer end-to-end approaches considering all the potential delay and error sources and proper statistical tools and methodologies are inevitably required for providing strong reliability and latency guarantees. This paper contributes to the body of knowledge in the latter aspect by providing a tutorial on several statistical tools and methodologies that are useful for designing and analyzing URLLC systems. Specifically, we overview the frameworks related to i) reliability theory, ii) short packet communications, iii) inequalities, distribution bounds, and tail approximations, iv) rare events simulation, vi) queuing theory and information freshness, and v) large-scale tools such as stochastic geometry, clustering, compressed sensing, and mean-field games. Moreover, we often refer to prominent data-driven algorithms within the scope of the discussed tools/methodologies. Throughout the paper, we briefly review the state-of-the-art works using the addressed tools and methodologies, and their link to URLLC systems. Moreover, we discuss novel application examples focused on physical and medium access control layers. Finally, key research challenges and directions are highlighted to elucidate how URLLC analysis/design research may evolve in the coming years.

翻译：超可靠低延迟通信（URLLC）构成了第五代及未来蜂窝网络的关键服务类别。值得注意的是，由于根本性需要识别并准确表征系统运行所依赖的统计模型（例如干扰统计量、信道条件及协议行为），URLLC的设计与支持极具挑战性。通常，需要采用考虑所有潜在时延与差错源的多层端到端方法，并辅以适当的统计工具及方法论，以提供强大的可靠性与时延保障。本文通过提供关于若干有助于设计与分析URLLC系统的统计工具和方法论的教程，为该领域的知识体系做出贡献。具体而言，我们概述了以下框架：i) 可靠性理论，ii) 短包通信，iii) 不等式、分布界与尾部近似，iv) 稀有事件仿真，v) 排队论与信息新鲜度，以及vi) 大规模工具（如随机几何、聚类、压缩感知与平均场博弈）。此外，我们经常在所讨论的工具/方法论范围内提及突出的数据驱动算法。贯穿全文，我们简要回顾了使用所涉及工具与方法论的最新研究成果，及其与URLLC系统的关联。同时，我们讨论了侧重于物理层与媒体接入控制层的新型应用实例。最后，强调了关键研究挑战与方向，以阐明未来数年内URLLC分析与设计研究可能如何演进。