Probabilistic End-to-End Delay Analysis for UAV-Assisted Integrated Terrestrial and Non-Terrestrial 6G Networks

Achieving ultra-reliable and low-latency communication (URLLC) in integrated terrestrial networks (TNs) and non-terrestrial networks (NTNs) is essential for the advancement of 6G networks. However, there is a significant lack of theoretical tools for analyzing probabilistic end-to-end (E2E) delay in such integrated networks. This analysis is crucial for estimating URLLC delay threshold violations and ensuring compliance with URLLC delay requirements. To address this gap, this paper introduces a systematic approach based on stochastic network calculus (SNC) utilizing moment-generating functions (MGFs) to compute the E2E delay violation probability for target traffic in unmanned aerial vehicles (UAVs) assisted integrated TNs and NTNs. The unique aspects of this scenario include two components: (1) TNs using conventional ground base stations, and (2) NTNs employing UAVs to relay data to ground base stations or high-altitude platform stations (HAPS). Our approach enhances the calculation of MGFs for service processes by considering transmission failures and blockages over sub-6 GHz and mmWave fading channels. This improvement offers a more precise performance characterization and facilitates the derivation of a closed-form expression for the upper-bounded statistical delay violation probability. Numerical results confirm that UAVs are advantageous in ensuring E2E delay guarantees by facilitating line-of-sight (LOS) transmission. Additionally, we provide insightful observations for resource allocation strategies in UAV-assisted integrated TNs and NTNs.