  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significance, as the use of outdated data may lead to unforeseeable or even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.
