# A Study on Safety Evaluation of Pedestrian Flows Based on Partial Impact Dynamics by Real-Time Data in Subway Stations

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## Abstract

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## 1. Introduction

## 2. Methodology and Models

#### 2.1. Characteristics Analysis

**1. Strategic level.**Behavior on the strategic levels refers to the intention made by pedestrians according to their needs which is the internal motivation to generate movement [33]. Generally, pedestrians in subway stations have a specific purpose such as making a ride, transferring between trains, or purchasing tickets. Compared with pedestrian flow in other scenarios, pedestrians in subway stations have more definite destinations or target behaviors. Therefore, we assume that pedestrians have pre-defined origins and destinations in subway stations; that is, they have definite OD (O-Origin, D-Destination). Note that if pedestrians are at an intermediate station on their journey, they too have a definite OD (origin and destination of transfer) [34].

**2. Tactical level.**The tactical level includes the behaviors that pedestrians make to achieve the goals set at the strategic level, which are affected by external and personal factors [33]. The input to the tactical level is the behavior of the strategy level; that is, the definite OD of pedestrians in subway stations. Specifically, pedestrians have already defined their origins and destinations and now need to perform route choice behavior at the tactical level. The factors that influence pedestrians’ route choice behaviors are summarized as: economy (charges, operating expenses), time (travel time, queue time), environment (congestion, queue length), and individual (age, personal habits) [35]. We assume that time factors influence pedestrians’ route choice behavior in subway stations because they are driven by a definite OD. Some scholars [36,37] similarly choose the shortest travel time to constrain the route choice behavior of pedestrians. Therefore, on the tactical level, we define the behavior of pedestrians as choosing the route that minimizes travel time.

**3. Operational level.**The operational level is the specific behavior of pedestrians that is performed to achieve targets based on the tactical level [33]. The decisions made at tactical levels serve as the inputs for pedestrians’ operational levels and determine their walking behaviors. The fact that pedestrians at subway stations choose the route with the shortest time makes pedestrians willing to ignore unimportant factors to achieve their goals. For example, pedestrian flow in subway stations is high during peak hours, and it is common for pedestrians to crowd each other [38]. Typically, pedestrians expect to keep a certain spatial distance from others [39]. However, in subway stations, pedestrians are willing to tolerate mutual crowding to reach their destinations quickly, and the space required for individuals can be compressed. The tolerance of squeezing behavior among pedestrians in subways is much greater than in other traffic settings such as intersections and pedestrian crossings. Moreover, pedestrians in subway stations are less sensitive to avoiding obstacles than in other scenarios and are reluctant to avoid such barriers in advance. Some scholars [38,40] also claim that pedestrians choose to ignore secondary factors to achieve their primary target. Thus, the behavior at the operational level includes high tolerance of pedestrian contact and low sensitivity behavior with regard to obstacles.

#### 2.2. Behavior Model

#### 2.2.1. Social Force Model

#### 2.2.2. Self-Driving Force

#### 2.2.3. Force on Pedestrians

#### 2.2.4. Force on Obstacles

#### 2.2.5. Force on Signs

#### 2.3. Risk Evaluation

**1. Construction of hierarchical structure.**We construct a three-level structure model consisting of target level, criterion level, and element level. The fluctuation of pedestrians is mainly caused by the interference of external environments [44]. After being disturbed, pedestrians’ behavior fluctuates in temporal and spatial dimensions. The movement time and speed provide valuable information for behavior analysis [45] and reflect the degree of interference. Similarly, travel distance and crowd density intuitively describe the behavior state and reflect the influence of interference on pedestrian behavior [46]. Therefore, we choose movement time and speed to represent the temporal fluctuation, while travel distance and crowd density show the spatial fluctuation. We define the element level factors as indicators describing the pedestrian fluctuation (FI) acquired by dynamic information of pedestrians in stations. Figure 2 shows the hierarchy of risk evaluation.

**2. Calculation of elements’ weights.**In the hierarchical structure, it is necessary to determine the importance of different elements in the target. In addition, the elements’ weights are determined by the calculation of the comparative judgment matrix. AHP introduces the numbers from 1–9 as the scale to characterize the relative importance of two elements for the target, enabling the construction of a comparative judgment matrix. The study quantifies the extent of FI for risk evaluation, and Table 2 gives comparative judgment matrices for temporal and spatial FI, respectively. Subsequently, we adopt the square root method to calculate the comparative judgment matrix of FI and obtain element weights. The square root method is commonly used to calculate the relative importance of elements through the judgment matrix. The calculation steps are as follows: (1) multiply the elements of the judgment matrix by rows to obtain a new vector; (2) take each component of the new vector to the n power; (3) normalize the obtained vector to be the weight vector. The equation for weight calculation is shown in (14). Figure 2 shows the symbols and weights of FI.

**3. Quantitative analysis of elements.**We assign values to FI and evaluates the risk to pedestrians on a quantitative level. We use numbers 1–5 to indicate levels of FI risk in descending order, so that higher quantitative values represent higher levels of risk. Table 3 shows the quantification of FI for the risk evaluation.

- The delay of movement time is the difference between the actual movement time of pedestrians and the ideal time, representing the efficiency of behaviors.
- The fluctuation of movement speed is the difference between the actual movement speed of pedestrians and their average speed, which denotes speed uniformity.
- The offset of travel distance is the difference between the actual walking path of pedestrians and the shortest possible path and indicates the fluctuation of trajectory.
- The crowd density is the number of pedestrians per unit area, expressing the objective environment during movement.

**4. Rating evaluation of risk.**We introduce the indicator of fluctuation risk index (FRI) to evaluate the risk of pedestrians. The FRI measures pedestrian risk from the temporal/spatial fluctuations dimension, and takes values in the range [1,5]. The equation is given in Equation (15). Specifically, a larger FRI shows a higher risk to pedestrians, when different levels of safety measures need to be taken to ensure their safety. We divide the risk rating into five classes. Table 4 identifies the relationship between FRI and risk levels and establishes a reference form for safety evaluation.

#### 2.4. Overall

## 3. Experiments and Results

#### 3.1. Simulations

#### 3.1.1. Model Validation

**1. Verification of improved self-driving force.**The PI-SFM considers the pedestrian characteristic of definite OD, making the self-driving force an essential factor driving pedestrians to move. As can be seen in Table 6, the average self-driving force of the PI-SFM is significantly higher than that of the SFM, suggesting that the PI-SFM better accounts for the self-driving force. Because the PI-SFM incorporates the OD factor affecting pedestrian speed, the correlation between speed and self-driving force is enhanced from weak to vigorous, reflecting the positive effect of self-driving force on speed. We also observe an increase in mean movement speed, but a decrease in the variance of pedestrian speed. The change in the measure of speed indicates that a strong self-driving force drives pedestrians to move toward their destinations with high speed and low-fluctuation walking behavior. Figure 5 shows the two models’ pedestrian-behavior range simultaneously. The range of pedestrian behavior is defined as the area covered by all pedestrians, showing in the red circles in Figure 5. It can be seen intuitively that the behavior range of the PI-SFM is significantly smaller than that of the SFM. In the PI-SFM, pedestrians tend to move closer to their destinations, being driven by the self-driving force. The number of pedestrians at the exit has increased, showing a gathering state. Therefore, it is clear that the improvement described in this paper with respect to self-driving force is reasonable and more consistent with the characteristics of pedestrians in subway stations.

**2. Verification of improved force on pedestrians.**The PI-SFM takes advantage of subway pedestrians’ high tolerance of mutual crowding. From Table 6, it can be seen that the exit density of the PI-SFM is noticeably higher than that of the SFM. We find that the PI-SFM allows for a moderate squeeze between pedestrians, reducing the required space for pedestrians and enabling adequate utilization of the area. Meanwhile, average movement times and travel distances are also reduced accordingly, due to the reduced spatial requirement. Figure 6a,b present simulations of pedestrians at the exit for both models. For purposes of comparison, we recall that the PI-SFM allows for contact between pedestrians. Figure 6c shows congregation of pedestrians at the exit in the PI-SFM simulation. A comparison of the two models indicates that the PI-SFM better simulates the crowding behavior on pedestrians, which results from the characteristics of the pedestrians. Hence, this study offers a reasonable assessment of the improvement of force on pedestrians.

**3. Verification of improved force on obstacles.**The PI-SFM better reflects how pedestrians are affected by obstacles with the need to make minor detours. Table 6 shows that the movement times and travel distances of the PI-SFM are effectively reduced compared to the SFM because it weakens the role of forces with respect to obstacles and shortens the detour distance of pedestrians. In the PI-SFM, pedestrians can reach their destination with a shorter walking distance and lower movement time, and their detour distance in the event of obstacles is effectively reduced. Figure 6d depicts the pedestrian contact with the wall at the exit for the PI-SFM, thereby reproducing the phenomenon of fewer detours to blocks. It can be readily appreciated that this improvement in modelling concerning the avoidance of obstacles is reasonable.

**4. Verification of improved force on signs.**The PI-SFM includes the attraction of indication signs to pedestrians, which prompts them to have a definite orientation to their destinations. In the simulation, we set the indication signs at the goal’s location to highlight the characteristic of pedestrians having a definite OD so that the uniqueness of pedestrian behaviors in subway stations can be manifested. The position of the sign means the pedestrians have a clear destination target to aim for. Both the self-driving force and the force on signs direct pedestrians to their destinations in the PI-SFM, driving pedestrians to move toward their goal with a firm intention. Figure 5 depicts the phenomenon of pedestrians converging upon their shared destination under the guidance of signs. Therefore, the average movement speed is improved, the movement time is reduced, and the force on signs is improved.

#### 3.1.2. Sensitivity Analysis

#### 3.2. Case Study

#### 3.3. Discussion

## 4. Conclusions

- Based on normative pedestrian behavior theory, we elaborate on pedestrian behavior at the strategic, tactical, and operational levels, principally by incorporating the characteristics of pedestrians with a definite OD.
- We propose a force model with partial impact (PI-SFM) based on a consideration of the influence of forces in the existing SFM. Four force influence mechanisms are defined to constrain the social forces and so describe the behavior of pedestrians in subway stations, namely, self-driven forces, forces on pedestrians, forces on walls, and forces on signs.
- We use real-time dynamic data to evaluate the risk to pedestrians. The influencing factors of pedestrian volatility are speed, time, distance, and crowd density. A hierarchical evaluation of pedestrian risk was achieved based on the proposed FRI.

## Author Contributions

## Funding

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Evolution of pedestrian behavior over time based on PI-SFM. The times were 0 s, 5 s, 10 s, and 20 s.

**Figure 6.**Crowd simulation in models. (

**a**,

**b**) show pedestrian behavior at the exit in the SFM and PI-SFM, respectively; (

**c**,

**d**) show pedestrian and obstacle contact behavior in the PI-SFM.

Year | Place | Description | Consequence |
---|---|---|---|

2019 | Mexico City, Mexico | an escalator did not stop in time, resulting in congestion of passengers at the elevator entrance | two people were slightly injured |

2018 | Rome, Italy | pedestrians disrupted the operation of an escalator | a severe stampede injured thirty people |

2018 | London, England | staff handled a suspicious package and caused a small explosion, and people crowded in panic | a chaotic situation resulted in five injuries |

2017 | Shenzhen, China | a passenger collapsed, resulting in pedestrians crowding and rushing each other | pedestrians were thrown into a significant panic |

2017 | Mumbai, India | at the peak of passenger flow, people were crowded and pushed | 22 personal deaths were caused |

Temporal Fluctuation | Spatial Fluctuation | |
---|---|---|

Temporal fluctuation | 1 | 2 |

Spatial fluctuation | 1/2 | 1 |

T | V | |

T | 1 | 2 |

V | 1/2 | 1 |

S | P | |

S | 1 | 4 |

P | 1/4 | 1 |

5 | 4 | 3 | 2 | 1 | |
---|---|---|---|---|---|

T | serious delay | high delay | obvious delay | a little delay | no delay |

V | severe fluctuations | high fluctuations | obvious fluctuations | a little fluctuation | no fluctuations |

S | serious deviation | high deviation | obvious deviation | a little deviation | no deviation |

P | severe congestion | high congestion | obvious congestion | a little congestion | no congestion |

Risk Level | Color | FRI | Risk Evaluation |
---|---|---|---|

Level 1 | blue | 1–2 | Basic security, no need to take measures |

Level 2 | green | 2–3 | General risk, take certain safety measures |

Level 3 | yellow | 3–3.5 | Moderate risk, safety measures should be taken |

Level 4 | orange | 3.5–4 | High risk, take safety measures as soon as possible |

Level 5 | red | 4–5 | High risk, take immediate safety measures |

Symbol | Description | Value |
---|---|---|

${m}_{i}$ | mass of the pedestrian | $80\mathrm{kg}$ |

${r}_{i}$ | the radius of the pedestrian model | $U\left(0.39,0.51\right)$ |

${\tau}_{i}$ | characteristic time | $0.5\mathrm{s}$ |

${A}_{i}$ | coefficient of repulsive interaction force | $2000\mathrm{N}$ |

${B}_{i}$ | coefficient of repulsive interaction force | $0.08\mathrm{m}$ |

$k$ | coefficient of body force | $1.2\times {10}^{5}\mathrm{kg}/{\mathrm{s}}^{2}$ |

$\u04a1$ | coefficient of sliding friction force | $2.4\times {10}^{5}\mathrm{kg}/\left(\mathrm{m}\xb7\mathrm{s}\right)$ |

Measure | Unit | SFM | PI-SFM |
---|---|---|---|

Average movement time, $\overline{t}$ | $\mathrm{s}$ | 43.23 | 31.78 |

Average movement speed, $\overline{v\left(t\right)}$ | $\mathrm{m}/\mathrm{s}$ | 1.12 | 1.46 |

Average travel distance, $\overline{s}$ | $\mathrm{m}$ | 48.42 | 46.40 |

Exit density, $\rho $ | $\mathrm{people}/{\mathrm{m}}^{2}$ | 0.83 | 2.13 |

Variance of movement speed, $var\left(v\left(t\right)\right)$ | $\mathrm{m}/\mathrm{s}$ | 0.55 | 0.32 |

Average self-driving force, $\overline{{f}_{will}}$ | $\mathrm{N}$ | 22.47 | 30.09 |

The coefficient of correlation between speed and self-driving force, $\mu $ | - | 0.46 | 0.73 |

Movement Speed | Movement Time | Travel Distance | Area Density | |
---|---|---|---|---|

Real experiment | 1.26 | 8.93 | 11.26 | 2.11 |

SFM | 1.36 | 10.31 | 13.89 | 0.77 |

PI-SFM | 1.29 | 8.20 | 10.57 | 2.65 |

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## Share and Cite

**MDPI and ACS Style**

Wang, X.; Zhang, Z.; Wang, Y.; Yang, J.; Lu, L.
A Study on Safety Evaluation of Pedestrian Flows Based on Partial Impact Dynamics by Real-Time Data in Subway Stations. *Sustainability* **2022**, *14*, 10328.
https://doi.org/10.3390/su141610328

**AMA Style**

Wang X, Zhang Z, Wang Y, Yang J, Lu L.
A Study on Safety Evaluation of Pedestrian Flows Based on Partial Impact Dynamics by Real-Time Data in Subway Stations. *Sustainability*. 2022; 14(16):10328.
https://doi.org/10.3390/su141610328

**Chicago/Turabian Style**

Wang, Xianing, Zhan Zhang, Ying Wang, Jun Yang, and Linjun Lu.
2022. "A Study on Safety Evaluation of Pedestrian Flows Based on Partial Impact Dynamics by Real-Time Data in Subway Stations" *Sustainability* 14, no. 16: 10328.
https://doi.org/10.3390/su141610328