In backbone networks, it is fundamental to quickly protect traffic against any unexpected event, such as failures or congestions, which may impact Quality of Service (QoS). Standard solutions based on Segment Routing (SR), such as Topology-Independent Loop-Free Alternate (TI-LFA), are used in practice to handle failures, but no distributed solutions exist for distributed and tactical congestion mitigation. A promising approach leveraging SR has been recently proposed to quickly steer traffic away from congested links over alternative paths. As the pre-computation of alternative paths plays a paramount role to efficiently mitigating congestions, we investigate the associated path computation problem aiming at maximizing the amount of traffic that can be rerouted as well as the resilience against any 1-link failure. In particular, we focus on two variants of this problem. First, we maximize the residual flow after all possible failures. We show that the problem is NP-Hard, and we solve it via a Benders decomposition algorithm. Then, to provide a practical and scalable solution, we solve a relaxed variant problem, that maximizes, instead of flow, the number of surviving alternative paths after all possible failures. We provide a polynomial algorithm. Through numerical experiments, we compare the two variants and show that they allow to increase the amount of rerouted traffic and the resiliency of the network after any 1-link failure.

翻译：在骨干网络中，快速保护流量免受任何意外事件（如可能影响服务质量的故障或拥塞）的影响至关重要。基于段路由的标准解决方案（如拓扑无关无环备用路径）在实践中用于处理故障，但尚无分布式解决方案用于分布式和战术性拥塞缓解。近期提出了一种利用SR的可行方法，通过替代路径快速将流量从拥塞链路疏导。由于替代路径的预计算对有效缓解拥塞起着关键作用，我们研究了相关的路径计算问题，旨在最大化可重路由的流量量以及应对任意单链路故障的韧性。具体来说，我们聚焦于该问题的两个变体。首先，在所有可能故障后最大化剩余流量。我们证明该问题为NP难问题，并通过Benders分解算法求解。其次，为提供实用且可扩展的解决方案，我们求解一个松弛变体问题，该问题不最大化流量，而是最大化所有可能故障后存活的替代路径数量。我们给出多项式算法。通过数值实验，比较两个变体并表明它们能在任意单链路故障后增加重路由流量量及网络韧性。