Stochastic Delay Analysis for Satellite Data Relay Networks with Heterogeneous Traffic and Transmission Links

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.