# A Dynamic Regional Partitioning Method for Active Traffic Control

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## Abstract

**:**

## 1. Introduction

## 2. Dynamic Defining Method of Regional Boundaries

#### 2.1. Methods for Selecting Benchmark Intersections

#### 2.2. Integrated Correlation Degree Model of Boundary Definition-Related Indicators

## 3. Models for Dynamically Defining Regional Boundaries

## 3.1. Preliminary Definition of Regional Boundaries

- (1)
- Intersection cycle

- (2)
- Intersection distance

- (1)
- By turning intersections into nodes and the road segments between them into edges, the complexity of the supplied traffic network is simplified;
- (2)
- The traffic information at the network’s nodes and edges is collected and tallied, then it is substituted into the correlation degree calculation model to determine the correlation degree between adjacent intersections;
- (3)
- The $N$ nodes are divided into separate communities by the initialized community network;
- (4)
- The array $A$ and the auxiliary matrix $F$, which contains all of the entries ${e}_{hm}$ and ${g}_{hm}$, are defined and initialized;
- (5)
- The combined pair of nodes connected by edges is used to calculate the update modularity increment as shown by Equation (7);
- (6)
- As the $n-1$ mergers are carried out, the procedure (5) is continued until the network is fully integrated. The community network is divided as a result, and the best community networks may be created by choosing the ${Q}_{w}$ value that maximizes modularity.

## 3.2. Proposed Regional Boundary Definition Method Based on Spectral Clustering

- (1)
- Division of the cut set control area

- (2)
- Similarity matrix

- (3)
- Road network node division

## 4. Model Validation and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Control boundaries of spectral clustering algorithm (

**a**), intersection group hierarchical clustering algorithm (

**b**), and boundary control subzone delineation method (

**c**).

Number | Path Number | w | Number | Path Number | w |
---|---|---|---|---|---|

1 | 1–2 | 0.58 | 12 | 8–9 | 0.83 |

2 | 2–3 | 0.48 | 13 | 9–10 | 0.95 |

3 | 3–4 | 0.43 | 14 | 10–11 | 0.13 |

4 | 4–5 | 0.49 | 15 | 12–13 | 0.63 |

5 | 1–6 | 0.67 | 16 | 13–14 | 0.27 |

6 | 2–7 | 0.32 | 17 | 14–15 | 0.64 |

7 | 3–9 | 0.76 | 18 | 6–12 | 0.24 |

8 | 4–10 | 0.78 | 19 | 7–13 | 0.38 |

9 | 5–11 | 0.77 | 20 | 9–14 | 0.44 |

10 | 6–7 | 0.41 | 21 | 10–15 | 0.36 |

11 | 7–8 | 0.81 | 22 | 11–15 | 0.31 |

**Table 2.**Common period and phase difference within the control boundary under the spectral clustering algorithm.

Quarters Number | Intersection Number | Common Cycle (s) | Phase Difference (s) |
---|---|---|---|

1 | 5 | 113 | 82 |

11 | 48 | ||

2 | 3 | 130 | 97 |

4 | 112 | ||

7 | 54 | ||

8 | 78 | ||

9 | 115 | ||

10 | 0 | ||

3 | 1 | 118 | 45 |

2 | 9 | ||

6 | 98 | ||

4 | 14 | 112 | 39 |

15 | 110 | ||

5 | 12 | 126 | 74 |

13 | 47 |

**Table 3.**Common period and phase difference within the control boundary under the intersection group hierarchical clustering algorithm.

Quarters Number | Intersection Number | Common Cycle (s) | Phase Difference (s) |
---|---|---|---|

1 | 5 | 113 | 81 |

11 | 49 | ||

2 | 3 | 130 | 97 |

4 | 112 | ||

9 | 115 | ||

10 | 0 | ||

14 | 16 | ||

15 | 47 | ||

3 | 7 | 122 | 0 |

8 | 24 | ||

4 | 1 | 115 | 45 |

6 | 98 | ||

7 | 7 | ||

5 | 12 | 126 | 74 |

13 | 47 |

**Table 4.**Common period and phase difference within the control boundary under the boundary control subarea division method.

Quarters Number | Intersection Number | Common Cycle (s) | Phase Difference (s) |
---|---|---|---|

1 | 5 | 113 | 82 |

11 | 48 | ||

2 | 3 | 130 | 97 |

4 | 112 | ||

7 | 54 | ||

8 | 78 | ||

9 | 115 | ||

10 | 0 | ||

3 | 1 | 115 | 45 |

6 | 98 | ||

7 | 7 | ||

4 | 12 | 126 | 74 |

13 | 47 | ||

14 | 99 | ||

15 | 53 |

Division Method | Regional Number | Average Stop of Vehicle (s) | Average Travel Time (s) | Queue Length (m) | Average Delay (s) |
---|---|---|---|---|---|

Spectral clustering algorithm | 5 | 1.96 | 1290 | 33 | 37.4 |

Intersection group hierarchical clustering algorithm | 5 | 2.23 | 1452 | 39 | 39.3 |

Boundary control subarea division method | 4 | 2.87 | 1681 | 48 | 41.7 |

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**MDPI and ACS Style**

Xing, Y.; Li, W.; Liu, W.; Li, Y.; Zhang, Z.
A Dynamic Regional Partitioning Method for Active Traffic Control. *Sustainability* **2022**, *14*, 9802.
https://doi.org/10.3390/su14169802

**AMA Style**

Xing Y, Li W, Liu W, Li Y, Zhang Z.
A Dynamic Regional Partitioning Method for Active Traffic Control. *Sustainability*. 2022; 14(16):9802.
https://doi.org/10.3390/su14169802

**Chicago/Turabian Style**

Xing, Yan, Wenqing Li, Weidong Liu, Yachao Li, and Zhe Zhang.
2022. "A Dynamic Regional Partitioning Method for Active Traffic Control" *Sustainability* 14, no. 16: 9802.
https://doi.org/10.3390/su14169802