Solving No-wait Scheduling for Time-Sensitive Networks with Daisy-Chain Topology

TL;DR

This paper presents an efficient polynomial-time algorithm for computing optimal no-wait schedules in Time-Sensitive Networking with daisy-chain topologies, addressing a key open problem in TSN scheduling.

Contribution

It introduces a novel polynomial-time algorithm for no-wait scheduling in daisy-chain TSN topologies by reformulating the problem as a restricted graph coloring task on interval graphs.

Findings

Algorithm scales polynomially with network size and number of streams.

Demonstrates optimal scheduling for real-life TSN systems with tens of thousands of streams.

Shows polynomial solvability of a restricted graph coloring problem on interval graphs.

Abstract

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.