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.

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