This article studies the reliability of multi-hop routing in a multi-tier hybrid satellite-terrestrial relay network (HSTRN). We evaluate the reliability of multi-hop routing by introducing interruption probability, which is the probability that no relay device (ground gateway or satellite) is available during a hop. The single-hop interruption probability is derived and extended to the multi-hop interruption probability using a stochastic geometry-based approach. Since the interruption probability in HSTRN highly depends on the priority of selecting communication devices at different tiers, we propose three priority strategies: (i) stationary optimal priority strategy, (ii) single-hop interruption probability inspired strategy, and (iii) density inspired strategy. Among them, the interruption probability under the stationary optimal priority strategy can approach the ideal lower bound. However, when analyzing an HSTRN with a large number of tiers, the stationary optimal priority strategy is computationally expensive. The single-hop interruption probability inspired strategy is expected to be a low-complexity but less reliable alternative to the stationary optimal priority strategy. In numerical results, we study the complementarity between terrestrial devices and satellites. Furthermore, analytical results for reliability are also applicable to the analysis of satellite availability, coverage probability, and ultra-reliable and low latency communications (URLLC) rate. Finally, we extend our original routing strategy into a multi-flow one with dynamic priority strategy.

翻译：本文研究了多层混合卫星地面中继网络（HSTRN）中多跳路由的可靠性。我们通过引入中断概率（即一跳过程中无中继设备（地面网关或卫星）可用的概率）来评估多跳路由的可靠性。基于随机几何方法推导出单跳中断概率，并进一步扩展至多跳中断概率。由于HSTRN的中断概率高度依赖于不同层级通信设备的选优优先级，我们提出了三种优先级策略：（i）静态最优优先级策略，（ii）单跳中断概率启发式策略，以及（iii）密度启发式策略。其中，静态最优优先级策略下的中断概率可逼近理论下界。然而，当分析包含大量层级的HSTRN时，静态最优优先级策略的计算复杂度较高。单跳中断概率启发式策略有望成为静态最优优先级策略的低复杂度但可靠性稍低的替代方案。数值结果中，我们研究了地面设备与卫星之间的互补性。此外，可靠性的分析结果同样适用于卫星可用性、覆盖概率以及超可靠低时延通信（URLLC）速率分析。最后，我们将原始路由策略扩展为采用动态优先级策略的多流路由策略。