Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Qian Li, Henan Liu, Heng Liu, Yuyi Wang

TL;DR

This paper develops 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.

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.

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

TL;DR

This paper develops 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.

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.
Paper Structure (10 sections, 5 theorems, 15 equations, 4 figures, 2 algorithms)

This paper contains 10 sections, 5 theorems, 15 equations, 4 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Notations and Mathematical Modeling
  4. Notations
  5. Recasting the no-wait scheduling problem as a graph coloring problem
  6. Algorithm Design
  7. Baby case: when all streams have the same period
  8. General case
  9. Evaluation
  10. Conclusion

Key Result

Theorem 3.1

There exists a no-wait schedule for $\mathcal{S}$ if and only if there is a good $p_{\mathcal{S}}$-coloring of $G_{\mathcal{S}}^\star$. Furthermore, a no-wait schedule can be easily obtained from a good $p_{\mathcal{S}}$-coloring.

Figures (4)

  • Figure 1: Illustration of the daisy-chain topology. Filled circles represent switches, and hollow ones represent end stations.
  • Figure 2: An Illustration of Gate Control List (GCL) from survey
  • Figure 3: (a) a set of streams $\mathcal{S}$; (b) routing paths; (c) $G_{\mathcal{S}}$; (d) $G^\star_{\mathcal{S}}$; (e) a Gantt chart describing a no-wait schedule; (f) a parallelogram (in green color); (g) a layer; (h) the Gantt chart description of each stream
  • Figure 4: The topology of the communication network on a metro train

Theorems & Definitions (13)

  • Theorem 3.1
  • Lemma 4.1
  • proof
  • Theorem 4.2
  • proof
  • Claim 4.3
  • Claim 4.4
  • Claim 4.5
  • proof
  • Remark 1
  • ...and 3 more