# Analysis of Crowded Propagation on the Metro Network

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Notations and Definitions

#### 2.2. Passenger Flow Allocation

#### 2.3. Passenger Flow Propagation Based on SIS Model

## 3. Experiment and Results

#### 3.1. The Initial Setting

#### 3.2. Spatiotemporal Analysis of Crowding Propagation

- (1)
- After the crowd occurs at some stations, it will spread to the majority of the network within half an hour. Then the propagation speed decreases and spreads throughout the network for about one and a half hours.
- (2)
- The propagation distance outward is limited, and the propagation strength decreases as the distance increases. The transfer nodes are more affected during propagation.

## 4. Discussion

## 5. Conclusions

- (1)
- Within half an hour, the majority of the network will become affected once it starts to happen at some stations. Following then, the propagation speed slows down.
- (2)
- The propagation strength diminishes with increasing distance. During propagation, the transfer nodes are significantly impacted.
- (3)
- Imposing control at the nodes with the highest demand or relatively peripheral nodes is more effective than other nodes.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 4.**The passing flow of Beijing metro network in morning rush hour. (

**a**) 7:00 to 8:00. (

**b**) 8:00 to 9:00.

Intervention Station Number | 14 | 23 | 25 | 35 | 43 | 44 | 116 |

Average RPC of the whole network among two hours | 0.185 | 0.190 | 0.184 | 0.190 | 0.191 | 0.189 | 0.190 |

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## Share and Cite

**MDPI and ACS Style**

Jia, C.; Zheng, S.; Qian, H.; Cao, B.; Zhang, K.
Analysis of Crowded Propagation on the Metro Network. *Sustainability* **2022**, *14*, 9829.
https://doi.org/10.3390/su14169829

**AMA Style**

Jia C, Zheng S, Qian H, Cao B, Zhang K.
Analysis of Crowded Propagation on the Metro Network. *Sustainability*. 2022; 14(16):9829.
https://doi.org/10.3390/su14169829

**Chicago/Turabian Style**

Jia, Cai, Shuyan Zheng, Hanqiang Qian, Bingxin Cao, and Kaiting Zhang.
2022. "Analysis of Crowded Propagation on the Metro Network" *Sustainability* 14, no. 16: 9829.
https://doi.org/10.3390/su14169829