SNC Analysis of End-to-End Delay in Cross-Media Tandem Links: An Acoustic-Radio Coupling Model

End-to-end (E2E) delay analysis is a prerequisite for protocol and algorithm design in water-air cross-media heterogeneous networks (WACHN). However, the heterogeneity of protocols and channels poses a significant challenge, as existing analytical methods cannot accommodate such diverse models. To address this gap, this work proposes a stochastic network calculus (SNC) based analytical framework for E2E delay in WACHN. Specifically, radio and underwater acoustic channel performance is characterized by modeling the relationship between channel quality and bit error rate using the three-ray and Thorp models. Furthermore, a Markov state transition service model is introduced for the underwater acoustic fountain code-based automatic repeat request mechanism, accounting for packet fragmentation, redundancy, and non-traffic conservation characteristics for the first time. Building on these models, this work quantifies the coupling effects of media switching, packet size variations, and slot-scale heterogeneity on E2E delay within the proposed SNC framework. Subsequently, a closed-form expression for the delay’s complementary cumulative distribution function (CCDF) is derived using martingale theory. To validate the theoretical derivation, Monte Carlo simulations demonstrate that analytical results accurately capture key statistical features such as distribution shape and tail behavior, validating the derived CCDF expression’s ability to provide a strict and effective delay upper bound. Consequently, the proposed framework establishes the first theoretical foundation for performance analysis and optimization of WACHN, comprehensively addressing media disparities.