# Time-of-Day Control Double-Order Optimization of Traffic Safety and Data-Driven Intersections

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. Procedural Framework

#### 3.2. First-Order Optimization (Model Construction of 3D Vector Time Division of Traffic Flow)

#### 3.2.1. Model Variable Definitions

#### 3.2.2. Calculation of Total Traffic Flow

#### 3.2.3. Calculation of Total Traffic Flow Direction

#### 3.2.4. The Calculation of the Traffic Safety Factor (Time Frequency Calculation with the Next Conflict Point Time)

#### 3.2.5. Construction of a 3D Vector Coordinate System

#### 3.2.6. Calculation of the Distance of the Adjacent 3D Vectors

#### 3.3. First-Order Optimization Algorithm Design

#### 3.3.1. Algorithm Flow

#### 3.3.2. Merging Rules of the Time Periods

#### 3.4. Second-Order Optimization (Model Adaptability Analysis of the Segmented Division Driven by Data)

#### 3.4.1. Selection of Input Data Source

#### Five-Number Summary

- Step 1:
- The data are arranged in ascending order.
- Step 2:
- The minimum value is confirmed.
- Step 3:
- The first quartile (Q1) is confirmed.
- Step 4:
- The median (Q2) is confirmed.
- Step 5:
- The third quartile (Q3) is confirmed.
- Step 6:
- The maximum value is confirmed.

#### A Five-Number Summary Method is Developed in this Study

- Step 1:
- The data are arranged in ascending order.
- Step 2:
- Five-number summary method is used to confirm five decision datasets.
- Step 3:
- In accordance with the five decision datasets in step 2, the data are initially divided into several peaks and a flat hump. The peak period is defined as the peak buffer period.
- Step 4:
- The average value in the peak buffer period is calculated.
- Step 5:
- The variance in the peak buffer period is calculated.
- Step 6:
- The maximum value in the peak buffer period is calculated.
- Step 7:
- The distance between the adjacent conflict points in the peak buffer period is calculated.

#### 3.4.2. Second-Order Optimization Algorithm Design

- Step 1:
- K observed values are randomly selected (each value is called a central point).
- Step 2:
- The distance/diversity of the observed value to each centre is calculated.
- Step 3:
- Each observed value is assigned to the nearest central point.
- Step 4:
- The sum of the distance from each of the central point to each observed value (total cost) is calculated.
- Step 5:
- A point in the class that is not the centre is selected and swapped with the centre point.
- Step 6:
- Each observed value is assigned to the nearest central point.
- Step 7:
- The total cost is recalculated.
- Step 8:
- If the total cost is less than the total cost calculated in step 4, then a new point is taken as the central point.
- Step 9:
- Steps 5 to 8 are repeated until the central point does not change.

## 4. Case Study

#### 4.1. Data Collection

#### 4.2. First-Order Optimization Simulation Evaluation

#### 4.2.1. Testing Data

#### 4.2.2. Simulation Platform and Testing Methods

#### 4.2.3. Evaluation Index

#### 4.3. Second-Order Optimization Simulation Evaluation

#### 4.3.1. Testing Data

#### 4.3.2. Data Clustering Analysis Simulation Evaluation

#### 4.3.3. Adaptability Analysis

- (1)
- Testing objective: To test the adaptability of the innovated method of time division into four intersection types
- (2)
- Testing data: Intersection data of the four types (155 in total)
- (3)
- Testing method: First-order optimization simulation evaluation
- (4)
- Evaluation index: Total delay time for the entire day (its calculation formula is the total time spent by cars waiting at the intersection) (unit: h)
- (5)
- Testing platform: The same system default control model based on Synchro 7

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Distribution chart of total and fractional flows of each direction (intersection of Yangming North Road and Renmin East Road, Yuecheng District, Shaoxing City on 23 June 2016).

**Figure 5.**Traffic flow and vector distribution diagram of the entire day (Intersection at Yangming North Road and Renmin East Road on 23 June 2016 on the basis of MATLAB).

**Figure 6.**Space distribution chart of the adjacent 3D vectors (entire-day traffic flow at the intersection of Yangming North Road and Renmin East Road in Shaoxing City on 23 June 2016).

**Figure 7.**Scheme comparison diagram of the 3D vector time period division with the traditional total flow division (entire-day traffic flow at the intersection of Yangming North Road and Renmin East Road in Shaoxing on 23 June 2016).

**Figure 9.**Scheme comparison diagram of the 3D vector time period division with the traditional total flow division (hump-type representative: No. 6 intersection of Jiefang South Road and South Ring Road).

**Figure 10.**Scheme comparison diagram of the 3D vector time period division with the traditional total flow division (constant-peak-type representative: No. 79 intersection at Pingjiang Road and Renmin East Road).

**Figure 11.**Scheme comparison diagram of the innovated time period division with the traditional total flow division (multi-peak-type representative: No. 61 intersection at Jiefang North Road and Renmin West Road).

**Table 1.**Time-of-day division scheme under the traditional total flow time period division of the intersection at Yangming North Road and Renmin East Road.

Serial No. of Time Period | Starting and Ending Times | Duration of the Time Period (h) | Total Delay Time of the Entire Day (h) |
---|---|---|---|

A | 6:00–10:00 | 4.0 | 12.35 |

B | 10:00–15:45 | 5.75 | 22.75 |

C | 15:45–19:45 | 4.0 | 24.5 |

D | 19:45–22:00 | 2.15 | 7.25 |

E | 22:00–6:00 | 8.0 | 7.15 |

Total | -- | 24 | 74.0 |

**Table 2.**Time-of-day division scheme under 3D vector time period division of the intersection at Yangming North Road and Renmin East Road.

Serial No. of Time Period | Starting and Ending Times | Duration of the Time Period (h) | Total Delay Time of the Entire Day (h) |
---|---|---|---|

A | 6:00–10:00 | 4.0 | 12.35 |

B | 10:00–12:30 | 2.5 | 7.25 |

C | 12:30–15:45 | 3.25 | 10.0 |

D | 15:45–19:45 | 4.0 | 24.5 |

E | 19:45–22:00 | 2.15 | 7.25 |

F | 22:00–6:00 | 8.0 | 7.15 |

Total | -- | 24 | 68.5 |

No. | Intersection Types | Average Value in the Peak Buffer Period | Variance in the Peak Buffer Period | Maximum Value in the Peak Buffer Period | First Quartile (Q1) | Third Quartile (Q3) |
---|---|---|---|---|---|---|

1 | Hump type | 241.734 | 350.123 | 359 | 70 | 315 |

2 | Constant-peak type | 613.796 | 5173.218 | 695 | 50 | 579 |

3 | Multi-peak model | 728.532 | 2803.248 | 803 | 181 | 753 |

**Table 4.**Adaptability analysis table of the four types of intersections by the innovated time period division.

No. | Intersection Types | Average Daily Delay under the Traditional Total Flow Time Division Method (h) | Average Daily Delay under the Innovated Flow Time Division Method (h) | Average Daily Delay Time within the Peak Buffer Period under the Traditional Total Flow Period Division Method (h) | Average Daily Delay Time within the Peak Buffer Period under the Innovated Time Division Method (h) |
---|---|---|---|---|---|

1 | Hump type | 91.375 | 86.235 | 26.75 | 22.2 |

2 | Constant peak type | 29.75 | 32.61 | 23.78 | 27.03 |

3 | Multi-peak type | 25.43 | 26.87 | 13.817 | 14.653 |

Total | 146.555 | 145.715 | 64.347 | 63.883 |

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## Share and Cite

**MDPI and ACS Style**

Xu, C.; Dong, D.; Ou, D.; Ma, C.
Time-of-Day Control Double-Order Optimization of Traffic Safety and Data-Driven Intersections. *Int. J. Environ. Res. Public Health* **2019**, *16*, 870.
https://doi.org/10.3390/ijerph16050870

**AMA Style**

Xu C, Dong D, Ou D, Ma C.
Time-of-Day Control Double-Order Optimization of Traffic Safety and Data-Driven Intersections. *International Journal of Environmental Research and Public Health*. 2019; 16(5):870.
https://doi.org/10.3390/ijerph16050870

**Chicago/Turabian Style**

Xu, Chen, Decun Dong, Dongxiu Ou, and Changxi Ma.
2019. "Time-of-Day Control Double-Order Optimization of Traffic Safety and Data-Driven Intersections" *International Journal of Environmental Research and Public Health* 16, no. 5: 870.
https://doi.org/10.3390/ijerph16050870