Martingale Theory-Based Delay Bound Analysis for Multi-Hop Heterogeneous Satellite Networks

Satellite networks hold great promise for future 6G communications because of their benefits such as wide coverage and large capacity. Since the end-to-end (e2e) queuing delay is regarded as one key factor affecting the quality of service (QoS) in satellite networks, accurate delay prediction is a critically important topic. However, the delay prediction is complicated due to the irregular and time-varying features of inter-satellite links (ISLs) and satellite-ground links (SGLs), such as discontinuity and alternation. In this paper, we propose to establish the multi-node satellite-to-ground communication procedure as a multi-hop tandemly queuing model and present a heterogeneous heterogeneous multi-hop martingale model for queuing delay analysis. Due to the unique time-varying characteristics, we propose to model the SGL and ISL services as the stationary Markov processes using the Markov chain Monte Carlo approach. To match the intermittency and burstiness of traffic, the data arrival and service processes are handled using the Markov process. We propose to use a scaling factor for reflecting the heterogeneity of data processing capability, and then present a novel approach to ensure the stability condition requirement of the multi-hop system. Using the multi-hop heterogeneous martingale approach, the tight upper bounds of the delay and backlog in heterogeneous links are derived, and then precise delay prediction can be obtained. Finally, numerous simulations are conducted to demonstrate the effectiveness and accuracy of the proposed martingale method in analyzing the system delay and backlog when compared to the existing stochastic network calculus method.