Software-defined satellite-terrestrial integrated networks (SDSTNs) are seen as a promising paradigm for achieving high resource flexibility and global communication coverage. However, low latency service provisioning is still challenging due to the fast variation of network topology and limited onboard resource at low earth orbit satellites. To address this issue, we study service provisioning in SDSTNs via joint optimization of virtual network function (VNF) placement and routing planning with network dynamics characterized by a time-evolving graph. Aiming at minimizing average service latency, the corresponding problem is formulated as an integer nonlinear programming under resource, VNF deployment, and time-slotted flow constraints. Since exhaustive search is intractable, we transform the primary problem into an integer linear programming by involving auxiliary variables and then propose a Benders decomposition based branch-and-cut (BDBC) algorithm. Towards practical use, a time expansion-based decoupled greedy (TEDG) algorithm is further designed with rigorous complexity analysis. Extensive experiments demonstrate the optimality of BDBC algorithm and the low complexity of TEDG algorithm. Meanwhile, it is indicated that they can improve the number of completed services within a configuration period by up to 58% and reduce the average service latency by up to 17% compared to baseline schemes.

翻译：软件定义卫星-地面一体化网络（SDSTNs）被视为实现高资源灵活性和全球通信覆盖的一种有前景的范式。然而，由于低地球轨道卫星网络拓扑的快速变化以及星载资源有限，低延迟服务供给仍面临挑战。为解决此问题，我们通过联合优化虚拟网络功能（VNF）部署和路由规划来研究SDSTN中的服务供给问题，其中网络动态性由时变图刻画。以最小化平均服务延迟为目标，相应问题在资源、VNF部署和时隙流约束下被建模为整数非线性规划。由于穷举搜索难以处理，我们通过引入辅助变量将原问题转化为整数线性规划，进而提出一种基于Benders分解的分支割平面（BDBC）算法。为面向实际应用，进一步设计了基于时间扩展的解耦贪婪（TEDG）算法并进行了严格的复杂度分析。大量实验证明了BDBC算法的最优性和TEDG算法的低复杂度。同时，与基线方案相比，它们在一个配置周期内可提升多达58%的已完成服务数量，并降低多达17%的平均服务延迟。