Time-Sensitive Networking (TSN) is a set of standards aiming to enable deterministic and predictable communication over Ethernet networks. However, as the standards of TSN do not specify how to schedule the data streams, the main open problem around TSN is how to compute schedules efficiently and effectively. In this paper, we solve this open problem for no-wait schedules on the daisy-chain topology, one of the most commonly used topologies. Precisely, we develop an efficient algorithm that optimally computes no-wait schedules for the daisy-chain topology, with a time complexity that scales polynomially in both the number of streams and the network size. The basic idea is to recast the no-wait scheduling problem as a variant of a graph coloring problem where some restrictions are imposed on the colors available for every vertex, and where the underlying graph is an interval graph. Our main technical part is to show that this variant of graph coloring problem can be solved in polynomial time for interval graphs, though it is NP-hard for general graphs. Evaluations based on real-life TSN systems demonstrate its optimality and its ability to scale with up to tens of thousands of streams.

翻译：时间敏感网络（TSN）是一套旨在实现以太网确定性可预测通信的标准集。然而，由于TSN标准未规定数据流的调度方法，其核心开放问题在于如何高效且有效地计算调度方案。本文针对最常用拓扑结构之一的菊花链拓扑，解决了无等待调度的这一开放问题。具体而言，我们提出了一种高效算法，能够以多项式时间复杂度（在流数量与网络规模上均呈多项式增长）为菊花链拓扑最优计算无等待调度方案。其基本思想是将无等待调度问题重新表述为图着色问题的变体，其中每个顶点可用的颜色受到特定限制，且基础图为区间图。我们的主要技术贡献在于证明：虽然该图着色问题变体在一般图上属于NP难问题，但对于区间图可在多项式时间内求解。基于实际TSN系统的评估验证了该算法的最优性及其处理数万条数据流的可扩展能力。