The satellite data relay networks (SDRNs) hold great promise in 6G communications for the timely offloading of the global traffic. Since the delay performance is regarded as one of the most important metrics reflecting the offloading efficiency, studying its relationship with network parameters becomes really essential to the development and application of the SDRN. However, the complex data offloading process and heterogeneity of traffic arrivals and transmission links pose many challenges to the stochastic delay analysis. To accurately model the data offloading process in SDRNs, we build a series-parallel queuing model with through and cross traffic while considering the propagation delay. On this basis, we respectively propose a propagation delay embedded min-plus convolution method based on stochastic network calculus and a Markov chain method based on Monte Carlo to depict the leftover services of the heterogeneous links received by the per-flow traffic in an aggregate. To eliminate the impacts of the heterogeneity, we uniformly characterize the arrivals and leftover services by their moment generating functions (MGFs) which contain the full moment information, and shield the heterogeneity by deriving the envelopes of the arrivals and leftover services with the help of MGFs, Chernoff bound and union bound. Then, in the light of the geometric relationship between the envelopes of the arrivals and leftover services, we analyze the upper bounds of the stochastic delay, which provides the guidance to the network configuration. Eventually, simulation results verify the effectiveness of the theoretical analysis and further reveal maximum four times the delay difference between the heterogeneous links influenced by traffic type, burstiness, and access number.

中文翻译：

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具有异构业务和传输链路的卫星数据中继网络的随机延迟分析


卫星数据中继网络 (SDRN) 在 6G 通信中为及时卸载全球流量带来了巨大希望。由于时延性能被认为是反映卸载效率的最重要指标之一，因此研究其与网络参数的关系对于SDRN的开发和应用至关重要。然而，复杂的数据卸载过程以及流量到达和传输链路的异构性给随机延迟分析带来了许多挑战。为了准确地模拟 SDRN 中的数据卸载过程，我们构建了一个具有直通和交叉流量的串并联排队模型，同时考虑了传播延迟。在此基础上，我们分别提出了基于随机网络演算的传播延迟嵌入最小加卷积方法和基于蒙特卡罗的马尔可夫链方法来描述每流流量接收到的异构链路的剩余服务。为了消除异质性的影响，我们通过包含完整矩信息的矩生成函数（MGF）来统一表征到达和剩余服务，并通过MGF的帮助导出到达和剩余服务的包络来屏蔽异质性、切尔诺夫约束和联合约束。然后，根据到达业务和剩余业务包络线之间的几何关系，分析随机时延的上限，为网络配置提供指导。最终，仿真结果验证了理论分析的有效性，并进一步揭示了流量类型、突发性和接入数对异构链路间最大时延差异的四倍影响。