Higher-Order Meta Distribution Reliability Analysis of Wireless Networks

Communication reliability, as defined by 3GPP, is the probability of achieving a desired quality of service (QoS). Traditionally, this metric is evaluated by averaging the QoS success indicator over spatiotemporal random variables. Recently, the meta distribution (MD) has emerged as a two-level analysis tool that characterizes system-level reliability as a function of link-level reliability thresholds. However, existing MD studies have two limitations. First, they focus exclusively on spatial and temporal randomness corresponding to node distribution and fading channels, respectively, leaving stochastic behaviors in other domains largely unexplored. Second, they are restricted to first-order MDs with two randomness levels, restricting applicability to scenarios requiring higher-order MD characterization. To address these gaps, we propose a hierarchical framework for higher-order MD reliability in wireless networks, where each layer’s success probability is formulated and fed into the next layer, yielding overall MD reliability at the highest level. We apply this framework to wireless networks by capturing three levels of temporal dynamics representing fast, slow, and static random elements, and provide a comprehensive second-order MD reliability analysis for two application scenarios. The effectiveness of the proposed approach is demonstrated via these representative scenarios, supported by detailed analytical and numerical evaluations. Our results highlight the value of hierarchical MD representations across multiple domains and reveal the significant influence of inner-layer target reliabilities on overall performance.