# A Primer on Design Aspects and Recent Advances in Shuffle Exchange Multistage Interconnection Networks

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## Abstract

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## 1. Introduction

#### 1.1. Related Surveys and Motivation

#### 1.2. Contribution

- It reviews the recent technical contributions towards improving fault-tolerance, analysis, assessment, and modelling of the reliability property of shuffle exchange MINs while comparing some of their key metrics, objectives and features. Topologies for enhanced SEN designs are also provided to facilitate a deeper understanding of the reviewed works.
- It highlights further recommendations towards the design and analysis of shuffle exchange networks based on lessons learnt from prior art and current research trends.

## 2. Multistage Interconnection Networks

#### 2.1. Architecture of MINs

#### 2.2. Categories of MINs

#### 2.3. Design Aspects of MINs

#### Improving Efficiency in MINs

#### 2.4. Shuffle Exchange MINs

## 3. Fault Tolerance

#### 3.1. Improving Fault Tolerance

#### Recent Advances

## 4. Reliability

#### 4.1. Reliability Measurement

#### Recent Advances

#### 4.2. Reliability Modelling

#### Recent Advances

#### 4.3. Reliability Assessment

#### Recent Advances

## 5. Future Recommendations

#### 5.1. Configuration

#### 5.2. Cost-Effectiveness

#### 5.3. Congestion

#### 5.4. Traffic

#### 5.5. Scalability

#### 5.6. Practical Assumptions

#### 5.7. Switching

#### 5.8. Performance Analysis

#### 5.9. Network Optimization

#### 5.10. Deadlock Avoidance

#### 5.11. Application to NOC

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**A three stage shuffle exchange network [35].

**Figure 6.**The fault-tolerant SEN- architecture [23].

**Figure 7.**Two layer replicated MINs proposed in [20].

**Figure 8.**(

**a**) Typical series reliability block diagram (RBD) configuration; (

**b**–

**d**) series-parallel RBD configurations.

**Figure 9.**Enhanced augmented shuffle-exchange network proposed in [1].

**Figure 11.**Parallel shuffle-exchange network [26].

Aspects | References | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

[1] | [20] | [21] | [6] | [22] | [23] | [24] | [25] | [26] | [27] | ||

Metric/Objective | Cost | • | • | ✓ | ✓ | • | • | • | • | ✓ | ✓ |

Delay | • | • | • | ✓ | • | • | • | • | • | • | |

Latency | • | • | • | • | • | ✓ | ✓ | ✓ | • | • | |

Complexity | • | • | • | ✓ | • | • | • | ✓ | • | • | |

Reliability | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | • | ✓ | ✓ | |

Fault-tolerance | • | • | • | ✓ | • | ✓ | ✓ | ✓ | ✓ | ✓ | |

Feature | Min. Path set Graph | • | • | • | • | ✓ | • | • | • | • | • |

Logic graph | • | • | • | • | ✓ | • | • | • | • | • | |

MUX/DEMUX | ✓ | • | ✓ | ✓ | • | ✓ | • | • | ✓ | ✓ | |

Loop | ✓ | • | • | • | • | • | • | • | • | • | |

Replication/Parallelism | ✓ | ✓ | • | • | • | • | • | • | ✓ | • | |

Stage+ | • | • | • | • | • | • | ✓ | • | ✓ | • | |

Stage− | • | • | • | • | ✓ | • | ✓ | • | • | ✓ | |

Re-arranged link | • | • | • | ✓ | • | • | • | • | • | • | |

Multi-internal path | ✓ | • | ✓ | • | • | • | • | • | ✓ | • | |

Disjoint path | • | • | • | • | • | ✓ | • | • | • | • | |

Bi-directional | • | • | • | • | ✓ | • | • | • | • | • | |

Broadcast | • | • | • | • | ✓ | • | • | ✓ | ✓ | ✓ | |

Multicast | • | • | ✓ | • | • | • | • | ✓ | • | • | |

New Fabric | • | • | • | • | • | • | ✓ | • | • | • |

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**MDPI and ACS Style**

Amodu, O.A.; Othman, M.; Yunus, N.A.M.; Hanapi, Z.M.
A Primer on Design Aspects and Recent Advances in Shuffle Exchange Multistage Interconnection Networks. *Symmetry* **2021**, *13*, 378.
https://doi.org/10.3390/sym13030378

**AMA Style**

Amodu OA, Othman M, Yunus NAM, Hanapi ZM.
A Primer on Design Aspects and Recent Advances in Shuffle Exchange Multistage Interconnection Networks. *Symmetry*. 2021; 13(3):378.
https://doi.org/10.3390/sym13030378

**Chicago/Turabian Style**

Amodu, Oluwatosin Ahmed, Mohamed Othman, Nur Arzilawati Md Yunus, and Zurina Mohd Hanapi.
2021. "A Primer on Design Aspects and Recent Advances in Shuffle Exchange Multistage Interconnection Networks" *Symmetry* 13, no. 3: 378.
https://doi.org/10.3390/sym13030378