# An Enhanced Routing and Scheduling Mechanism for Time-Triggered Traffic with Large Period Differences in Time-Sensitive Networking

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## Abstract

**:**

## 1. Introduction

#### 1.1. Contributions

- We preprocess the preknown flows and group them based on the period correlation to obtain a delimited set of flows, named flow classification (FC).
- Based on the FC, a multiperiod flows routing and scheduling algorithm (MPFRS-FC) adopts the iterated ILP-based scheduling and routing in order to attain high scheduling scalability by flow group, and incrementally adding a flow group to the scheduled procedure is proposed. Additionally, the link pruning after successful scheduling of each flow group in the MPFRS-FC can effectively reduce the search space and execution time.
- Furthermore, an adaptive period compensation routing and scheduling algorithm based on FC (APCRS-FC) is designed to tackle the simple or loosely coupled network topology carrying complex periodic TT traffic problems, since multiple disjoint paths need to be found in the MPFRS-FC algorithm to minimize the number of unschedulable flows.
- Through evaluations, the paper shows that the proposed algorithm outperforms benchmark routing and scheduling algorithms in terms of scheduling success rate and execution time.

#### 1.2. Outline of the Paper

## 2. Background and Related Work

## 3. System Model

#### 3.1. Network Model

#### 3.2. Flow Specification

## 4. Proposed Solution

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

**Proof**

**of**

**Definition 3**

Algorithm 1: Flows classification algorithm |

#### 4.1. Routing Constraints

#### 4.2. Schedule Constraints

**Contention Constraints:**To achieve zero congestion transmission, it is required that all assigned time slots are nonoverlapping. For any two flows ${f}_{m}$, ${f}_{k}$, no flow can be sent to the same link at the same time, otherwise, a conflict occurs. The forward time of outgoing ports of each switch does not conflict. We have the condition

**Transmission Cycle Constraints:**The flow must be transmitted during its cycle and cannot be confused with the next cycle. The transmission start time of the flow ${f}_{k}$ on the link ${v}_{i},{v}_{j}$ is constrained by:

**Path Order Constraints:**Only when the flow is received by the current node, the previous node can start to transmit the next flow. Hence, the constraint is

**No-wait Forwarding Constraints:**We assume that each switch forwards a data frame immediately after it is received, while satisfying the path constraint above.

#### 4.3. Application Constraints

#### 4.4. Objective Function

Algorithm 2: Multiperiod flow routing and scheduling algorithms with flow classification |

Algorithm 3: An adaptive period compensation routing and scheduling with flow classification |

## 5. Evaluations

#### 5.1. Experiment Setup

- Optimal: One suboptimal schedule was found (scheduling as much flow as possible is the pursuit of this paper rather than the optimal solution).
- Timeout: The time limit was reached before the schedule was found.
- Infeasible: No schedule was found with the given flows.

#### 5.2. Performance Evaluation

#### 5.2.1. Performance versus Traffic Load

#### 5.2.2. Performance versus Traffic Type

#### 5.2.3. Performance versus Network Scale

#### 5.2.4. Performance versus Network Type

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Example TSN topology model $G(16,21)$ including ten end systems which schedule six types of flows via six switches with multiple no-conflict paths. A controller collects application information and network topology information and reports to scheduler module. The schedule results can be deployed on the TSN devices.

**Figure 2.**A scenario where four time-triggered flows traverse through one route $[s{w}_{0},s{w}_{2},$ and $s{w}_{4}]$ generated by SRP routing algorithm.

**Figure 3.**Schedule for three flows on the $s{w}_{0}$’s output port. The squares symbolize transmission time slots for the respective flow on the link $(s{w}_{0}4$ and $s{w}_{2})$.

**Figure 4.**Synthetic topology test cases. (

**a**) A small ring topology. (

**b**) A small mesh topology. (

**c**) A medium ring topology. (

**d**) A medium mesh topology.

**Figure 6.**Percentage distribution of optimal, timeout, and infeasible instances of SPRF-EtoED, LBF-EtoED, MPFRS-FC, and APCRS-FC for different network topos and different number of flows. (

**a**) Topo 1: small ring. (

**b**) Topo 2: small mesh. (

**c**) Topo 3: medium ring. (

**d**) Topo 4: medium mesh.

**Figure 7.**Maximum execution time and average execution time for the SPRF-EtoED, LBF-EtoED, MPFRS-FC, and APCRS-FC for 100 synthetic test cases with different number of flows, tested in SM network. (

**a**) Flows chosen from flow group 1. (

**b**) Flows chosen from flow group 2.

**Figure 8.**Maximum execution time and average execution time for the SPRF-EtoED, LBF-EtoED, MPFRS-FC, and APCRS-FC for 100 synthetic test cases with different number of flows, tested in MM network. (

**a**) Flows chosen from flow group 1. (

**b**) Flows chosen from flow group 2.

**Figure 9.**Success rate and the sum of end-to-end delays of the SPRF-EtoED, LBF-EtoED, MPFRS-FC, and APCRS-FC for 100 synthetic test cases with different number of flows chosen from flow group 2, tested in SM network. (

**a**) Technique 1: SPRF-EtoED. (

**b**) Technique 2: LBF-EtoED. (

**c**) Technique 3: MPFRS-FC. (

**d**) Technique 4: APCRS-FC.

**Figure 10.**Success rate and the sum of end-to-end delays of the SPRF-EtoED, LBF-EtoED, MPFRS-FC, and APCRS-FC for 100 synthetic test cases with different number of flows chosen from flow group 2, tested in MM network. (

**a**) Technique 1: SPRF-EtoED. (

**b**) Technique 2: LBF-EtoED. (

**c**) Technique 3: MPFRS-FC. (

**d**) Technique 4: APCRS-FC.

**Figure 11.**Percentage of solved, timeout, and infeasible schedules and execution time of the SPRF-EtoED, LBF-EtoED, MPFRS-FC, and APCRS-FC for 100 test cases with 20 flows, tested in MM network. (

**a**) Technique 1: SPRF-EtoED. (

**b**) Technique 2: LBF-EtoED. (

**c**) Technique 3: MPFRS-FC. (

**d**) Technique 4: APCRS-FC.

**Figure 12.**The sum of end-to-end delays of the SPRF-EtoED, LBF-EtoED, MPFRS-FC, and APCRS-FC for 100 test cases with 20 flows, tested in MM network.

**Figure 13.**Percentage of solved, timeout, and infeasible schedules and execution time of the SPRF-EtoED, LBF-EtoED, MPFRS-FC, and APCRS-FC for 100 test cases with 40 flows chosen from flow group 1, tested in MM network. (

**a**) Technique 1: SPRF-EtoED. (

**b**) Technique 2: LBF-EtoED. (

**c**) Technique 3: MPFRS-FC. (

**d**) Technique 4: APCRS-FC.

**Figure 14.**The sum of end-to-end delays of the SPRF-EtoED, LBF-EtoED, MPFRS-FC, and APCRS-FC for 100 test cases with 30 flows chosen from flow group 2, tested in different types of network.

Notation | Description | |
---|---|---|

$index$ | $i,j,x,y,z$ | the index of a node |

$k,m$ | the index of a flow | |

$[i,j]$ | the index of a link | |

l | the index of a link | |

$set$ | V | the vertex set |

E | the edge set | |

$ES$ | the set of all end systems | |

$SW$ | the set of all switches | |

F | the set of all flows | |

$vector$ | ${\mathbf{src}}^{\mathbf{F}}$ | source vector |

${\mathbf{dest}}^{\mathbf{F}}$ | destination vector | |

${\mathbf{prd}}^{\mathbf{F}}$ | period vector | |

${\mathbf{td}}^{\mathbf{F}}$ | transmission duration vector | |

$\omega $ | transmission window offset vector | |

$decision\phantom{\rule{4pt}{0ex}}variable$ | $\mathbf{r}$ | route decision vector |

$\phi $ | time slot offset vector |

Flow Index | F.prd/$\mathsf{\mu}$s | F.td/$\mathsf{\mu}$s | Probability |
---|---|---|---|

F1 | 100 | 1 | $1/5$ |

F2 | 200 | 2 | $1/5$ |

F3 | 40 | 4 | $1/5$ |

F4 | 80 | 8 | $1/5$ |

F5 | 160 | 8 | $1/5$ |

Flow Index | F.prd/$\mathsf{\mu}$s | F.td/$\mathsf{\mu}$s | Probability |
---|---|---|---|

F1 | 100 | 1 | $1/4$ |

F2 | 200 | 2 | $1/4$ |

F3 | 400 | 2 | $7/40$ |

F4 | 49 | 1 | $1/40$ |

F5 | 50 | 1 | $3/10$ |

Flow Index | F.prd/$\mathsf{\mu}$s | F.td/$\mathsf{\mu}$s | Probability |
---|---|---|---|

F1 | 143 | 1 | $1/40$ |

F2 | 130 | 1 | $1/40$ |

F3 | 500 | 2 | $1/4$ |

F4 | 100 | 2 | $9/20$ |

F5 | 250 | 1 | $1/4$ |

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**MDPI and ACS Style**

Nie, H.; Li, S.; Liu, Y. An Enhanced Routing and Scheduling Mechanism for Time-Triggered Traffic with Large Period Differences in Time-Sensitive Networking. *Appl. Sci.* **2022**, *12*, 4448.
https://doi.org/10.3390/app12094448

**AMA Style**

Nie H, Li S, Liu Y. An Enhanced Routing and Scheduling Mechanism for Time-Triggered Traffic with Large Period Differences in Time-Sensitive Networking. *Applied Sciences*. 2022; 12(9):4448.
https://doi.org/10.3390/app12094448

**Chicago/Turabian Style**

Nie, Hongrui, Shaosheng Li, and Yong Liu. 2022. "An Enhanced Routing and Scheduling Mechanism for Time-Triggered Traffic with Large Period Differences in Time-Sensitive Networking" *Applied Sciences* 12, no. 9: 4448.
https://doi.org/10.3390/app12094448