Deterministic routing has emerged as a promising technology for future non-terrestrial networks (NTNs), offering the potential to enhance service performance and optimize resource utilization. However, the dynamic nature of network topology and resources poses challenges in establishing deterministic routing. These challenges encompass the intricacy of jointly scheduling transmission links and cycles, as well as the difficulty of maintaining stable end-to-end (E2E) routing paths. To tackle these challenges, our work introduces an efficient temporal graph-based deterministic routing strategy. Initially, we utilize a time-expanded graph (TEG) to represent the heterogeneous resources of an NTN in a time-slotted manner. With TEG, we meticulously define each necessary constraint and formulate the deterministic routing problem. Subsequently, we transform this nonlinear problem equivalently into solvable integer linear programming (ILP), providing a robust yet time-consuming performance upper bound. To address the considered problem with reduced complexity, we extend TEG by introducing virtual nodes and edges. This extension facilitates a uniform representation of heterogeneous network resources and traffic transmission requirements. Consequently, we propose a polynomial-time complexity algorithm, enabling the dynamic selection of optimal transmission links and cycles on a hop-by-hop basis. Simulation results validate that the proposed algorithm yields significant performance gains in traffic acceptance, justifying its additional complexity compared to existing routing strategies.

翻译：确定路由已成为未来非地面网络（NTN）中一项前景广阔的技术，有望提升服务性能并优化资源利用率。然而，网络拓扑和资源的动态特性给建立确定路由带来了挑战，包括联合调度传输链路与时隙的复杂性，以及维持稳定端到端（E2E）路由路径的困难性。为应对这些挑战，本文提出了一种基于时间图的高效确定路由策略。首先，我们利用时变扩张图（TEG）以时隙方式表示NTN中的异构资源。基于TEG，我们细致定义了各项必要约束并建立了确定路由问题的数学表述。随后，将该非线性问题等价转化为可求解的整数线性规划（ILP），提供一种稳健但耗时的高性能上限。为降低问题求解复杂度，我们引入虚拟节点和虚拟边对TEG进行扩展，从而统一表示异构网络资源与流量传输需求。由此提出一种多项式时间复杂度算法，能够在逐跳基础上动态选择最佳传输链路与时隙。仿真结果表明，与现有路由策略相比，所提算法在流量接纳方面具有显著性能增益，验证了其额外复杂度的合理性。