As one of the pivotal enablers for 6G, satellite-terrestrial integrated networks have emerged as a solution to provide extensive connectivity and comprehensive 3D coverage across the spatial-aerial-terrestrial domains to cater to the specific requirements of 6G massive ultra-reliable and low latency communications (mURLLC) applications, while upholding a diverse set of stringent quality-of-service (QoS) requirements. In the context of mURLLC satellite services, the concept of data freshness assumes paramount significance, as the use of outdated data may lead to unforeseeable or even catastrophic consequences. To effectively gauge the degree of data freshness for satellite-terrestrial integrated communications, the notion of age of information (AoI) has recently emerged as a novel dimension of QoS metrics to support time-sensitive applications. Nonetheless, the research efforts directed towards defining novel diverse statistical QoS provisioning metrics, including AoI, delay, and reliability, while accommodating the dynamic and intricate nature of satellite-terrestrial integrated environments, are still in their infancy. To overcome these problems, in this paper we develop analytical modeling formulations/frameworks for statistical QoS over 6G satellite-terrestrial integrated networks using hybrid automatic repeat request with incremental redundancy (HARQ-IR) in the finite blocklength regime. In particular, first we design the satellite-terrestrial integrated wireless network architecture model and AoI metric model. Second, we characterize the peak-AoI bounded QoS metric using HARQ-IR protocol. Third, we develop a set of new fundamental statistical QoS metrics in the finite blocklength regime. Finally, extensive simulations have been conducted to assess and analyze the efficacy of statistical QoS schemes for satellite-terrestrial integrated networks.
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