In segment routing, a packet is forwarded along a path identified by a segment list. A segment list consists of segment identifiers (SIDs). A node-SID identifies a shortest-path segment, and an adjacency-SID identifies a link segment. A K{K} -segment path is a path with no more than K{K} segments. In this paper, we study the problem of finding a set of K-segment paths to carry all the flows in a given traffic matrix such that the maximum link utilization in the network is minimized. We first show that the solutions found by K{K} -LP, an existing linear programming (LP) approach, are not optimal because K{K} -LP does not support adjacency-SIDs. Focusing on 2-segment paths, a new LP formulation, denoted by e2-LP, is designed to support adjacency-SIDs in part. To fully support adjacency-SIDs, a mixed integer linear programming (MILP), denoted by K{K} -MILP, is designed. Since solving K{K} -MILP is time-consuming, a simplified version ( K{K} -sMILP) is also proposed. Finally, K{K} -sMILP is extended to prevent excessive flow splitting or using paths that are too long.

中文翻译：

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使用 MILP 的分段路由网络中的流量工程


在分段路由中，数据包沿着由分段列表标识的路径转发。段列表由段标识符 (SID) 组成。节点SID标识最短路径段，邻接SID标识链路段。 AK{K} 段路径是不超过 K{K} 段的路径。在本文中，我们研究了寻找一组K段路径来承载给定流量矩阵中的所有流量的问题，从而最小化网络中的最大链路利用率。我们首先表明，现有的线性规划 (LP) 方法 K{K} -LP 找到的解决方案并不是最优的，因为 K{K} -LP 不支持邻接 SID。关注 2 段路径，一种新的 LP 公式（表示为 e2-LP）旨在部分支持邻接 SID。为了完全支持邻接SID，设计了混合整数线性规划（MILP），表示为K{K} -MILP。由于求解 K{K} -MILP 非常耗时，因此还提出了简化版本 ( K{K} -sMILP)。最后，K{K} -sMILP 被扩展以防止过度的流分裂或使用太长的路径。