# Urban Agglomeration High-Speed Railway Backbone Network Planning: A Case Study of Beijing-Tianjin-Hebei Region, China

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Research on the Current Situation of Beijing-Tianjin-Hebei Region

#### 2.2. Research on Node Importance

#### 2.3. Research on HSR Network Planning

#### 2.4. Research on DBSCAN

#### 2.5. Literature Analysis

- (1)
- Most of the literature analyzes the importance of nodes in a qualitative way and provides suggestions and guidance for the development direction. In the research of this paper, on the basis of the analysis of the current situation, the quantitative calculation is carried out, and the importance value of the city node is given. The conclusion is more accurate and targeted.
- (2)
- In the literature on the development status and network planning of the Beijing–Tianjin–Hebei region, it is found that the core cities in the Beijing–Tianjin–Hebei region drive the development trend of small- and medium-sized cities, the synergy between railway transportation capacity and economic development is poor. The existing literature raises questions after introducing the current situation, while there is very little content in high-speed rail network planning for the development status of urban agglomerations. Therefore, in the selection of indices and line network planning, we pay attention to the establishment of models based on the actual development situation and policy requirements, which is of great practical significance.
- (3)
- In the part of the city hierarchy division, this paper innovatively uses density-based noise to apply the spatial clustering method instead of the traditional clustering algorithm so that the calculation process does not use pre-labeled targets to cluster data points. The calculation results are not affected by outliers.

## 3. Beijing–Tianjin–Hebei Node Importance and Line Urgency

#### 3.1. Evaluation Model

#### 3.1.1. Evaluating Indices

#### 3.1.2. Node Importance Model

#### 3.1.3. Line Urgency Model

#### 3.2. Node Importance and Line Urgency Solution

#### 3.2.1. Index Weight

- (1)
- Initial data statistics. Seven characteristics of urban nodes are selected as the comprehensive evaluation index of node importance. The initial data are calculated and are obtained as shown in Table 1. The unit of passenger railway mileage is passenger–kilometer.
- (2)
- In order to eliminate the influence of different dimensions on the index calculation, they need to be processed forward. Therefore, it needs to be forward processed after the forward processing and then normalization of the index.
- (3)
- Calculate the mean (${\overline{z}}_{q}$) and standard deviation (${s}_{q}$) of the initial data for any metric q. Additionally, m is the number of city nodes. The equation is as follows:$${\overline{z}}_{q}=\frac{1}{m}{\displaystyle \sum _{i=1}^{m}{z}_{iq}}$$$${S}_{q}=\sqrt{\frac{{\displaystyle \sum _{i=1}^{m}({z}_{iq}-{\overline{z}}_{iq}{)}^{2}}}{m-1}}$$

- (4)
- Let the correlation coefficient matrix of the sample matrix be R. The corresponding eigenvalues and eigenvectors are calculated. Calculating the eigenvalues (${\lambda}_{t}$) and eigenvectors (${\rho}_{t}$), and n is the number of indexes.$$R=\left(\begin{array}{ccc}{r}_{11}& \dots & {r}_{1n}\\ \vdots & \ddots & \vdots \\ {r}_{n1}& \cdots & {r}_{nn}\end{array}\right)$$$$\left|R-{\lambda}_{t}I\right|=0$$$$(R-{\lambda}_{t}I){\rho}_{t}=0$$$${r}_{qo}=\frac{1}{m-1}{\displaystyle \sum _{i=1}^{m}({Z}_{iq}^{*}-{Z}_{io}^{*})}=\frac{1}{m-1}{\displaystyle \sum _{i=1}^{m}\frac{({z}_{iq}-{\overline{z}}_{q})({z}_{qo}-{\overline{z}}_{o})}{{S}_{q}{S}_{o}}}$$

- (5)
- KMO statistics and Bartlett’s sphericity test.

- (6)
- Common factor variance and component coefficient score calculation.

- (7)
- Determining eigenvalues, eigenvectors and selecting principal components.

- (8)
- Principal component factor gravel diagram analysis.

- (9)
- Determination of weight coefficient.

#### 3.2.2. Node Importance

#### 3.2.3. Line Urgency

## 4. Beijing–Tianjin–Hebei HSR Network Planning

#### 4.1. City Node Classification

- (1)
- Let the sample set be T, $T=\{{t}_{1},{t}_{2},\dots ,{t}_{13}\},{t}_{i}\in T,{N}_{\Im}({t}_{j})=\{{t}_{i}\subseteq T/d({t}_{i},{t}_{j})<\in \}$.$\left|{{\rm N}}_{\Im}({t}_{i})\right|$${t}_{i}$ belongs to the set T. If the neighborhood $\Im $ corresponds $\left|{N}_{\Im}({t}_{i})\right|$ and contains at least the $MinPts$$\left|{N}_{\Im}\left({t}_{i}\right)\right|>MinPts$${t}_{j}$ ${t}_{i}$.
- (2)
- The distance between the samples is measured. The radius distance between the core object and each sample is calculated. Through the sensitivity test, it is found that when the sample radius ($eps$) is 0.09. The minimum sample size is two, which can be selected.

- (3)
- Find a set of nodes whose density can reach all the core objects, which is a cluster.
- (4)
- Then, continue to repeat the steps of (3), there is no category of core objects to find the density of the node set.
- (5)
- Finally, all clusters are obtained. Using phyton software, until all core objects have categories. Its operation steps are shown in the Figure 3 algorithm flow chart.

#### 4.2. Main Backbone Line Planning Model

- (1)
- Coverage Constraints Between Adjacent Nodes.

- (2)
- Number Constraint of Main Backbone Lines.

- (3)
- Node Level Constraint.

- (4)
- Main Backbone Line Number Constraint.

- (5)
- Primary Network Size Constraints.

- (6)
- Non-Linear Coefficient.

#### 4.3. DBSCAN Design

_{0,}and the set of unselected backbone nodes is represented by V

_{1}. Then, the intercity railway main trunk line planning model of urban agglomeration is used to calculate whether the node is the main skeleton node by traversal algorithm. Finally, the adjacent nodes in the V

_{0}form and the main skeleton line group l

_{0,}which is the main trunk line.

#### 4.4. Analysis of Planning Results

- (1)
- Road Network Density.

- (2)
- The Proportion of Node GDP on the Main Trunk.

- (3)
- Population Coverage Rate.

- (4)
- HSR Coverage.

## 5. Conclusions

- (1)
- Through the quantitative analysis of the characteristics of urban nodes, the relative importance values of 13 urban nodes are calculated by means of node importance and line urgency model. Among them, Beijing and Tianjin are the highest, ranking first and second. At the same time, the urgency value of the HSR lines between any two cities among the 13 city nodes can be obtained.
- (2)
- Based on the value of node importance and line urgency, the DBSCAN is used to cluster the 13 urban nodes. It is found that the 13 cities in the Beijing–Tianjin–Hebei urban agglomeration can be divided into four levels, among which Beijing and Tianjin are located in the first-level urban nodes. Shijiazhuang, Qinhuangdao, Handan, Tangshan, Chengde and Cangzhou are located in the secondary city nodes. Additionally, the remaining cities are located in the third and fourth city nodes, which is in line with the relative situation of the comprehensive development level of cities in the urban agglomeration and intuitively reflects the relative status of each city node.
- (3)
- Combined with the development status of HSR network nodes and lines in urban agglomerations, a backbone selection model was constructed with the greatest urgency of the line. From the calculation results, it can be found that there are seven backbone lines in the Beijing–Tianjin–Hebei urban agglomeration, mainly covering eight secondary nodes, such as Beijing, Tianjin and Shijiazhuang. The line covers the existing lines, such as Beijing–Guangzhou, Beijing–Shanghai, Tianjin–Qinhuangdao and other major HSR lines in China. It basically covering the main development axes, such as Beijing–Tianjin, Beijing–Baoshi and Beijing–Tangshan, which can basically meet the railway transportation that attracts existing passenger flow. The four backbone lines of Beijing–Cangzhou, Beijing–Shijiazhuang-Baoding and Beijing–Tangshan selected in the new plan can take into account the passenger flow of the backbone line. At the same time, it realizes the role of driving and alleviating the operation of the branch line and realizes the backbone line as the core to accelerate the development of the internal traffic of the urban agglomeration and realize the construction goal of the hourly HSR.
- (4)
- The contribution of the adjusted main trunk line selection scheme. It can not only determine the layout of the railway network in the Beijing–Tianjin–Hebei urban agglomeration, alleviate the congestion of the branch passenger flow and ensure the stability of the operation but also improve the accessibility and coverage of the overall HSR network in the urban agglomeration. It provides direction and foreshadowing for the future urban spatial structure and economic development. In particular, when selecting the backbone line. This paper considers the importance of the node and the urgency of the line and innovatively uses the BDSCAN to comprehensively cluster the urban nodes to explore the potential development potential of the nodes. It is of surreal significance to supplement the branch lines and refine the line direction.
- (5)
- This paper has certain innovation and comprehensiveness in the method selection and factor consideration of the backbone line network planning of the urban agglomeration. However, due to the relatively high level of the selected 13 urban nodes, there are some limitations in the further site selection and feeder passenger flow distribution in the future. Considering the specific urban nodes at the county level and below, further refinement and supplement can be made in the node selection.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Index | Degree Centrality | Closeness Centrality | Betweenness Centrality | Flow Betweenness Centrality | Economic Relations | Transportation Capacity | Passenger Railway-Mileage | |
---|---|---|---|---|---|---|---|---|

City | ||||||||

BJ | 219 | 53.62 | 13 | 0.49 | 1478.44 | 5.75 | 1012.9 | |

TJ | 270 | 5.12 | 11 | 0.15 | 129.82 | 1.82 | 278.82 | |

SJK | 111 | 4.43 | 10 | 0.14 | 95.43 | 0.93 | 7.8 | |

TS | 95 | 4.48 | 10 | 0.02 | 15.86 | 0.53 | 11 | |

QHD | 85 | 2.79 | 10 | 0.07 | 1.04 | 0.48 | 6.2 | |

HD | 105 | 10.74 | 10 | 0.07 | 36.94 | 0.94 | 1 | |

XT | 56 | 5.17 | 9 | 0.05 | 3.5 | 0.29 | 13.2 | |

BD | 40 | 0.17 | 9 | 0.01 | 6.29 | 0.75 | 8.5 | |

ZJK | 6 | 0 | 2 | 0.01 | 0.28 | 0.69 | 4.9 | |

CD | 6 | 0 | 2 | 0.02 | 2.83 | 0.45 | 3.2 | |

CZ | 24 | 1.5 | 5 | 0.01 | 0 | 0.4 | 10.8 | |

LF | 8 | 0 | 2 | 0.01 | 0.3 | 0.62 | 4.9 | |

HS | 12 | 0 | 0 | 0 | 0 | 0.27 | 3 |

KMO Sampling Suitability Quantity | 0.725 | |

Bartlett Sphericity Test | Approximate Chi-square | 158.586 |

Degree of Freedom | 21 | |

Significance | 0.000 |

Initialization Value | Extraction Rate | |
---|---|---|

Var00001 | 1 | 0.613 |

Var00002 | 1 | 0.924 |

Var00003 | 1 | 0.436 |

Var00004 | 1 | 0.974 |

Var00005 | 1 | 0.914 |

Var00006 | 1 | 0.956 |

Var00007 | 1 | 0.936 |

Component | Initial Eigenvalue | Extract the Load Sum of Squares | ||||
---|---|---|---|---|---|---|

Grand total | Variance Proportion | Accumulative (%) | Grand Total | Variance Proportion | Accumulate (%) | |

1 | 5.755 | 82.221 | 82.221 | 5.755 | 82.221 | 82.221 |

2 | 0.947 | 13.524 | 95.746 | 0.000 | 0.000 | 0.000 |

3 | 0.231 | 3.294 | 99.040 | 0.000 | 0.000 | 0.000 |

4 | 0.034 | 0.490 | 99.530 | 0.000 | 0.000 | 0.000 |

5 | 0.021 | 0.302 | 99.832 | 0.000 | 0.000 | 0.000 |

6 | 0.010 | 0.143 | 99.975 | 0.000 | 0.000 | 0.000 |

7 | 0.002 | 0.025 | 100.000 | 0.000 | 0.000 | 0.000 |

Index (${\mathit{\omega}}_{\mathit{i}}$) | Degree Centrality | Closeness Centrality | Betweenness Centrality | Flow betweenness Centrality | Economic Relations | Transportation Capacity | Railway Passenger Turnover |
---|---|---|---|---|---|---|---|

Weight | 0.33 | 0.40 | 0.28 | 0.41 | 0.40 | 0.40 | 0.41 |

City | BJ | TJ | SJZ | TS | QHD | HD | XT | BD | ZJK | CD | CZ | LF |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Importance Value | 2.21 | 0.73 | 0.41 | 0.26 | 0.26 | 0.37 | 0.23 | 0.17 | 0.07 | 0.06 | 0.11 | 0.07 |

BJ | TJ | SJZ | TS | QHD | HD | XT | BD | ZJK | CD | CZ | LF | HS | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

BJ | 0.00 | 67,435.35 | 3884.26 | 6199.29 | 475.94 | 696.74 | 319.76 | 3057.71 | 386.19 | 209.60 | 997.91 | 8650.94 | 59.52 |

TJ | 67,435.35 | 0.00 | 396.84 | 1661.57 | 88.49 | 113.93 | 49.99 | 332.70 | 16.53 | 17.28 | 612.57 | 400.36 | 12.03 |

SJZ | 3884.26 | 396.84 | 0.00 | 36.96 | 4.88 | 140.62 | 111.21 | 126.65 | 3.55 | 1.16 | 24.32 | 9.07 | 9.86 |

TS | 6199.29 | 1661.57 | 36.96 | 0.00 | 52.09 | 12.10 | 5.10 | 22.25 | 2.49 | 7.31 | 20.84 | 24.54 | 0.90 |

QHD | 475.94 | 88.49 | 4.88 | 52.09 | 0.00 | 1.87 | 0.76 | 2.35 | 0.34 | 1.21 | 1.98 | 1.54 | 0.11 |

HD | 696.74 | 113.93 | 140.62 | 12.10 | 1.87 | 0.00 | 300.89 | 14.68 | 0.81 | 0.37 | 7.10 | 2.17 | 2.39 |

XT | 319.76 | 49.99 | 111.21 | 5.10 | 0.76 | 300.89 | 0.00 | 7.88 | 0.37 | 0.67 | 3.21 | 0.99 | 1.32 |

BD | 3057.71 | 332.70 | 126.65 | 22.25 | 2.35 | 14.68 | 7.88 | 0.00 | 0.74 | 0.24 | 5.78 | 3.65 | 0.73 |

ZJK | 386.19 | 16.53 | 3.55 | 2.49 | 0.34 | 0.81 | 0.37 | 0.74 | 0.00 | 0.16 | 0.46 | 0.64 | 0.05 |

CD | 209.60 | 17.28 | 1.16 | 7.31 | 1.21 | 0.37 | 0.67 | 0.24 | 0.16 | 0.00 | 0.85 | 1.24 | 0.05 |

CZ | 997.91 | 612.57 | 24.32 | 20.84 | 1.98 | 7.10 | 3.21 | 5.78 | 0.46 | 0.85 | 0.00 | 4.53 | 1.17 |

LF | 8650.94 | 400.36 | 9.07 | 24.54 | 1.54 | 2.17 | 0.99 | 3.65 | 0.64 | 1.24 | 4.53 | 0.00 | 0.20 |

HS | 59.52 | 12.03 | 9.86 | 0.90 | 0.11 | 2.39 | 1.32 | 0.73 | 0.05 | 0.05 | 1.17 | 0.20 | 0.00 |

Urban Hierarchy | Name of City Node |
---|---|

Primary City Node | BJ, TJ |

Secondary City Node | SJZ, QHD, HD, TS, CD, CZ |

Three-Level City Node | XT, HS |

Four-Level City Node | BD, ZJK, LF |

City | BJ | TJ | SJZ | QHD | HD | TS | CD | CZ | BD | Mean Value |
---|---|---|---|---|---|---|---|---|---|---|

region | 36,102.60 | 14,083.73 | 5935.1 | 1685.8 | 3636.6 | 7210.9 | 1550.3 | 3699.9 | 3954.3 | 10,799.14 |

City | BJ | TJ | SJZ | QHD | HD | TS | CD | CZ | BD | Mean Value |
---|---|---|---|---|---|---|---|---|---|---|

Population | 2153.6 | 1373 | 1124.15 | 313.98 | 941.49 | 771.85 | 335.15 | 730.22 | 1154.63 | 1112.26 |

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## Share and Cite

**MDPI and ACS Style**

Zhao, J.; Rong, W.; Liu, D.
Urban Agglomeration High-Speed Railway Backbone Network Planning: A Case Study of Beijing-Tianjin-Hebei Region, China. *Sustainability* **2023**, *15*, 6450.
https://doi.org/10.3390/su15086450

**AMA Style**

Zhao J, Rong W, Liu D.
Urban Agglomeration High-Speed Railway Backbone Network Planning: A Case Study of Beijing-Tianjin-Hebei Region, China. *Sustainability*. 2023; 15(8):6450.
https://doi.org/10.3390/su15086450

**Chicago/Turabian Style**

Zhao, Jun, Wenyu Rong, and Di Liu.
2023. "Urban Agglomeration High-Speed Railway Backbone Network Planning: A Case Study of Beijing-Tianjin-Hebei Region, China" *Sustainability* 15, no. 8: 6450.
https://doi.org/10.3390/su15086450