# Optimization Method for Conventional Bus Stop Placement and the Bus Line Network Based on the Voronoi Diagram

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Research method

#### 2.1. Division of Public Transport Service Community Based on Voronoi Diagram

#### 2.2. Generation of Candidate Station Set for Conventional Buses

- The location of candidate bus stations should give priority to the main sources of passengers, such as urban rail stations, business centers, transportation hubs, schools, hospitals, administrative units, residential areas, long-distance passenger stations, railway stations, etc.
- To facilitate passengers’ ride and transfer, the candidate stations are preferred near the intersection, but the delay time of bus vehicles, the interference to the intersection capacity and traffic flow, and the impact on pedestrian safety need to be fully demonstrated.
- If a station is set at the intersection of high-level and low-level roads, the station of its turning line shall be preferentially set on high-grade roads.
- The distance between the intermediate stops of the urban line and the suburban line of the conventional bus is 500–600 m and 800–1000 m, respectively, and the distance between the urban line and the suburban line of the large bus stop express is 1500–2000 m and 1500–2500 m, respectively.
- Within the polygonal service area, the repetition rate of 500 m coverage of two discrete points shall not exceed 40%. In the actual site selection process, after the alternative bus stop location is determined, the actual situation at the stop is known. The more passengers at the alternative station and the shorter the distance for passengers to reach the alternative station, the more reasonable the location and traffic direction of the road section.

#### 2.3. Establishment of Optimization Model

#### 2.3.1. Optimization Model for Conventional Bus Stop Placement

#### 2.3.2. Optimization Model for Conventional Bus Line Network

- Line network coverage

- 2.
- Collinearity with rail transit

- 3.
- Network station service rate

_{i}—number of bus trips in community served by conventional bus stop $i$;

- 4.
- Per capita travel time of residents from bus to rail transfer station

- 5.
- Line length

- 6.
- Non-linear coefficient of line

- 7.
- Direct passenger flow of the line

## 3. Empirical Research

#### 3.1. Instance Background

#### 3.2. Application of Optimization Method

#### 3.2.1. Placement Optimization of Conventional Bus Stops

#### 3.2.2. Optimization of Conventional Bus Line Network

- Display and analysis of optimization results of single service cell

#### 3.3. Optimization Results and Evaluation Analysis

## 4. Conclusions

- The concept of the Voronoi diagram was introduced into the field of public transport, and the average pedestrian arrival time of passengers was taken as the main consideration in setting up bus stops. A placement optimization method of conventional bus stops based on the Tyson model was proposed.
- Choosing the traditional test algorithm, aiming at the maximum coverage of the line network, the minimum collinearity with rail transit, the maximum service rate of line network stations and the minimum average transfer time from residents to rail stations, this study established the optimization model of the conventional bus network and puts forward the optimization method of the conventional bus network.
- Taking the Wuhan East Lake demonstration area as an example, the optimization method for the conventional bus transit system proposed in this study was applied to the study. The results show that this optimization method has obvious effects on selecting the connection and transfer hub between rail transit and conventional bus transit, and increasing the proportion of public transport travel.
- Two optimization schemes of five conventional bus lines in the Wuhan East Lake demonstration area are given. The results show that the bus line network coverage and station service rate have been significantly improved after optimization, and the bus route repetition coefficient and per capita transfer time have been significantly reduced. This shows that the research results of this study have practical reference value.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Regional status map of Wuhan East Lake demonstration area. (

**a**). The optimization scope. (

**b**). The regional road networks.

**Figure 4.**Passenger flow distribution map of conventional bus stops in the Wuhan East Lake demonstration area.

**Figure 6.**Distribution map of transfer communities between rail transit and conventional bus in the East Lake demonstration area.

**Figure 7.**Fitting diagram of the relationship between the proportion of passengers using the bus and the time required for arrival in the East Lake demonstration area.

**Figure 8.**Current land use distribution map of Liufangyuan Road community. (

**a**). The current stations. (

**b**). The range of origins.

**Figure 9.**Distribution of conventional bus stops within the affected area of the No. 32 transfer community.

**Figure 10.**Schematic diagram of conventional bus network data within the influence range of the No. 32 transfer community.

**Figure 11.**Distribution map of conventional bus feeder network within the influence area of the No. 32 transfer community.

The Acceptable Walking Time for Resident (Min) | $\le 1$ | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | $\ge 12$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Proportion | 100% | 85% | 74% | 62% | 53% | 46% | 32% | 24% | 18% | 13% | 9% | 7% |

Source Serial Number | Nature of Land Use | Floor Area (HA) | Plot Ratio | Incidence (Person/HA) | Number of Passengers (Person) | Time to Walk to the Bus Stop (Min) |
---|---|---|---|---|---|---|

1 | Land for scientific research and education | 31.6 | 1.68 | 210 | 11,148 | 3.6 |

2 | Land for scientific research and education | 12.4 | 1.55 | 170 | 3267 | 2.8 |

3 | Office land | 5.6 | 2.43 | 160 | 2177 | 1 |

4 | Office land | 5.3 | 2.65 | 150 | 2106 | 4.2 |

5 | Office land | 6.1 | 2.12 | 150 | 1939 | 3.2 |

Source Serial Number | 1 | 2 | 3 | 4 | 5 | Rail Station |
---|---|---|---|---|---|---|

Number of passengers (person) | 7357 | 2156 | 1436 | 1390 | 1280 | 1321 |

Walk to station time (min) | 3.6 | 2.8 | 1 | 4.2 | 3.2 | 2.2 |

Source Serial Number | 1 | 2 | 3 | 4 | 5 | Rail Station |
---|---|---|---|---|---|---|

Number of passengers (person) | 7357 | 2156 | 1436 | 1390 | 1280 | 1321 |

Walking time to station (min) | 4.9 | 4.6 | 2.1 | 5.3 | 1 | 0 |

**Table 5.**Index table of conventional bus feeder network within the affected area of the No. 32 transfer community.

Line Name | Origin–Destination | Straight Line Distance × 1.4 (km) | Shortest Path | Shortest Line Length (km) | Time of Minimum Line (Min) |
---|---|---|---|---|---|

No.333 | 1Y | 3.08 | 1-O-N-X-Y | 2.4 | 15 |

No.388 | 1T | 2.38 | 1-P-U-T | 2 | 11 |

No.753 | 1F | 1.96 | 1-J-E-F | 1.6 | 10 |

No.786 | 1A | 3.5 | 1-J-I-B-A | 3 | 16 |

**Table 6.**List of candidate routes of the conventional bus feeder network within the influence range of the No. 32 transfer community.

Line Name | Origin–Destination | Candidate Line | Line Length | Line Number |
---|---|---|---|---|

333 | 1Y | 1-O-N-X-Y | 2.4 | 1a |

1-V-W-X-Y | 2.9 | 1b | ||

1-V-W-O-N-X-Y | 3.6 | 1c | ||

1-J-L-O-N-Y | 3.7 | 1d | ||

388 | 1T | 1-P-U-T | 2 | 2a |

1-P-Q-U-T | 2.2 | 2b | ||

1-V-U-T | 2.3 | 2c | ||

1-J-G-M-S-T | 3.7 | 2d | ||

753 | 1F | 1-J-K-G-F | 3 | 3a |

1-L-D-E-F | 3.2 | 3b | ||

1-P-Q-K-G-F | 3.8 | 3c | ||

786 | 1A | 1-J-I-B-A | 3 | 4a |

1-L-I-B-A | 3.2 | 4b | ||

1-O-N-I-B-A | 3.2 | 4c | ||

1-J-L-C-B-A | 3.4 | 4d | ||

1-P-Q-K-J-I-B-A | 3.9 | 4e |

Network Coverage | Collinearity with Rail Transit | Line Network Station Service Rate | Per Capita Transfer Time (min) | |
---|---|---|---|---|

Original wire network | 39% | 2% | 89% | 19.6 |

Scheme 1 | 43% | 19% | 81% | 16.4 |

Scheme 2 | 51% | 16% | 95% | 14.7 |

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**MDPI and ACS Style**

Wang, F.; Ye, M.; Zhu, H.; Gu, D.
Optimization Method for Conventional Bus Stop Placement and the Bus Line Network Based on the Voronoi Diagram. *Sustainability* **2022**, *14*, 7918.
https://doi.org/10.3390/su14137918

**AMA Style**

Wang F, Ye M, Zhu H, Gu D.
Optimization Method for Conventional Bus Stop Placement and the Bus Line Network Based on the Voronoi Diagram. *Sustainability*. 2022; 14(13):7918.
https://doi.org/10.3390/su14137918

**Chicago/Turabian Style**

Wang, Fu, Manqing Ye, Hongbin Zhu, and Dengjun Gu.
2022. "Optimization Method for Conventional Bus Stop Placement and the Bus Line Network Based on the Voronoi Diagram" *Sustainability* 14, no. 13: 7918.
https://doi.org/10.3390/su14137918