Non-terrestrial networks (NTNs) are expected to provide continuous and ubiquitous connectivity across the globe. We identify that deterministic routing is a promising technology to achieve high resource utilization and strict QoE guarantee in NTNs. However, due to the time-varying topology, dynamic bandwidth and long propagation, for establishing deterministic services, it is not only difficult in finding stable end-to-end (E2E) routing, but also complex for joint routing and scheduling. Towards this, we propose an optimal solution based on temporal graphs to enhance resource utilization and service capability of NTNs. First, an extended time-expanded graph (ETEG) with introduced virtual nodes and edges is constructed to uniformly model both heterogeneous resources and traffic requirements. Then, we recast the deterministic routing problem as an integer linear programming (ILP) problem, by linearizing the constraints containing variable-dependent summations, round-down operation and multiplication of nonlinear terms. With the solid upper bound by ILP-based scheduling, we further propose a low-complexity ETEG-based shortest time-featured path algorithm to jointly use transmission and storage resources to support dynamic queuing and cross-cycle transmission of packets, thereby determining the best outgoing link and forwarding cycle hop-by-hop. The optimality and complexity are analyzed, together with simulations to verify the superiority of proposed algorithm in traffic acceptance, E2E delay and running time.

翻译：非地面网络（NTN）有望为全球提供连续、泛在的连接。我们发现确定性路由是一种在NTN中实现高资源利用率和严格QoE保障的颇具前景技术。然而，由于时变拓扑、动态带宽和长传播延迟，建立确定性服务不仅难以找到稳定的端到端（E2E）路由，而且联合路由和调度也极为复杂。为此，我们提出一种基于时间图的最优方案，以提升NTN的资源利用和服务能力。首先，构建包含虚拟节点和边的扩展时间扩展图（ETEG），对异构资源和流量需求进行统一建模。接着，通过线性化包含变量相关求和、向下取整操作和非线性项乘法的约束，将确定性路由问题重新表述为整数线性规划（ILP）问题。在ILP调度的坚实上界基础上，我们进一步提出一种低复杂度的基于ETEG的最短时间特征路径算法，联合使用传输和存储资源以支持数据包的动态排队和跨周期传输，从而逐跳确定最佳出站链路和转发周期。分析了算法的最优性和复杂度，并通过仿真验证了所提算法在流量接纳、E2E时延和运行时间方面的优越性。