# Smart-Guided Pedestrian Emergency Evacuation in Slender-Shape Infrastructure with Digital Twin Simulations

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## Abstract

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## 1. Introduction

## 2. Smart Guidance through Digital Twin Simulations

## 3. Digital Twin of Evacuation Process inside Slender-Shape Infrastructure

#### 3.1. Infrastructure Internal Space

#### 3.2. Pedestrian Movement Rules

_{th}pedestrian at time t and cell (x,y,t) denotes the status of the unit cell.

_{th}pedestrian’s position at time step t and step t + 1,

_{th}pedestrian moving out. The following equations depict the pedestrian position update, with pedestrians’ corresponding movement priority sequence indicated in Figure 3b,c for position near or at the exit gates, respectively.

#### 3.3. Evacuation Guiding Strategies

- (1)
- Strategy 1: fixed guidance according to geometry of the infrastructure internal space

_{th}pedestrian staying at cell (x,y) when the emergency accident occurs, his/her distance to the exit gates are:

_{th}pedestrian to Gate A or Gate B,

_{A}and G

_{B}are the x coordinates of the 2 exit gates shown in Figure 2. The pedestrian will be instructed to go to the nearest gate.

- (2)
- Strategy 2: smart guidance based on estimated evacuation time

_{N,f}denote the N

_{th}pedestrian’s estimated time to reach to the exit gate in free movement state, while T

_{N,c}the evacuation time the pedestrian required to leave the gate due to the existence of crowds around the gate area in obstructed movement state. At the instance of the emergency accident, for the N

_{th}pedestrian at cell $\left({x}_{\mathrm{N}},\text{}{y}_{N}\right)$, the distance of the pedestrian to the exit gates can be calculated according to Equation (7). If the free movement state occurs for the N

_{th}pedestrian and all the other pedestrians ahead of him/her to the selected exit gate, we can roughly make an estimation of the time required by all pedestrians to get out of the exit gate. The following formula can be obtained by ignoring delay arising from potential congestion during the evacuation process with movement velocity of 1-unit cell per time step.

_{th}pedestrian and all the other pedestrians ahead of him/her to the selected exit gate, due to existence of crowded area around the gate, we can use the following formula to estimate the time required for the pedestrian to evacuate through the exit gate:

_{th}pedestrian to the exit gate A or B; i is an integer among 0 to N

_{total}, which is every pedestrian’s ID number; and k is an empirical coefficient to adjust for the exit gate evacuation capacity and a function of localized pedestrian population density around the gate, with value ranges from 0 to 1. This is because the pedestrian movement flow is stochastic in nature, and the gate width only offers the upper bound estimation of the actual pedestrian flow rate. The actual flow rate will depend on the temporal and spatial characteristics of the pedestrian flow. Therefore, parameter k could be obtained and tuned through virtual simulations, or through analysis of accumulated monitoring data in the real project over time, based on statistics or machine learning techniques. However, a detailed discussion of this will be beyond the scope of this study. For the purpose of this paper, we assume k equals to 1, namely the upper boundary of the evacuation capacity.

_{th}pedestrian, whose estimated escaping time to gate A and gate B are the same, namely

_{th}pedestrian will be instructed to evacuate from Gate A, while pedestrians to the right to escape through Gate B.

## 4. Numerical Experiments

#### Simulation Initialization

## 5. Results and Discussions

## 6. Summary and Conclusions

- (a)
- In general, evacuation time increases with higher overall density for both guiding strategies. However, the smart-guided simulations tends to experience slower growth in evacuation time than that of the fixed guided ones for increased density settings, and thus more resilient to pedestrian population density change.
- (b)
- Different pedestrian crowd location also influences the total evacuation time, and the performance of the smart guided system is overall more immune to the influence of the position change of these regions in comparison with the fixed guided cases.
- (c)
- The smart-guided system is found to most obviously outperform the fixed-guided system in mid to high population densities (density around 0.3 to 0.5), which results in time saving ranging from 8.7% to 23.8%. In relative lower density settings, improvements of the smart guided system over fixed guided ones are not obvious.
- (d)
- Simulation results indicate that the smart guided system demonstrates smaller discrepancy over different simulation realizations, demonstrating more consistent results, and therefore a more robust guiding system.
- (e)
- A closer examination of the pedestrian evacuation behavior shows that the introduction of the smart guidance helps to more scientifically divide people to evacuate through respective exit gates so that crowds tend to dissipate simultaneously, and therefore, more evacuation capacity of the exit gates can be mobilized, resulting in shorter total evacuation time and improved safety for pedestrians collectively.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Pedestrian Movement Strategy Diagram. (

**a**) Far Away From Exit Gate; (

**b**) Near the Exit Gate; (

**c**) at the Exit Gate.

**Figure 5.**Pedestrian Movement Priority Diagram. (

**a**) Pedestrians Evacuate Through the Nearest Exit Gate; (

**b**) Pedestrians Evacuate Through Exit Gate Based on Estimated Evacuation Time.

**Figure 7.**Evacuation Time in Different Density Distribution Settings. (

**a**) Total Evacuation Time Under Fixed Guidance; (

**b**) Total Evacuation Time Under Smart Guidance; (

**c**) Total Time Saving; (

**d**) std. of Total Evacuation Time Under Fixed Guidance; (

**e**) std. of Total Evacuation Time Under Smart Guidance; (

**f**) std. of Total Time Saving.

**Figure 8.**Evacuation Simulations at Particular Density Settings. (

**a**) Pedestrians at Gate Areas Under Fixed Guidance (Point A); (

**b**) Pedestrians Leaving the Infrastructure Under Fixed Guidance (Point A); (

**c**) Pedestrians at Gate Areas Under Smart Guidance (Point A); (

**d**) Pedestrians Leaving the Infrastructure Under Smart Guidance (Point A); (

**e**) Pedestrians at Gate Areas Under Fixed Guidance (Point B); (

**f**) Pedestrians Leaving the Infrastructure Under Fixed Guidance (Point B); (

**g**) Pedestrians at Gate Areas Under Smart Guidance (Point B); (

**h**) Pedestrians Leaving the Infrastructure Under Smart Guidance (Point B); 15% Saving of Total Evacuation Time is Achieved for Smart-Guided Evacuations Over Fixed-Guided Ones for Point A Density Combination, while 7% is Obtained for Point B Density Settings.

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**MDPI and ACS Style**

Han, T.; Zhao, J.; Li, W.
Smart-Guided Pedestrian Emergency Evacuation in Slender-Shape Infrastructure with Digital Twin Simulations. *Sustainability* **2020**, *12*, 9701.
https://doi.org/10.3390/su12229701

**AMA Style**

Han T, Zhao J, Li W.
Smart-Guided Pedestrian Emergency Evacuation in Slender-Shape Infrastructure with Digital Twin Simulations. *Sustainability*. 2020; 12(22):9701.
https://doi.org/10.3390/su12229701

**Chicago/Turabian Style**

Han, Tianran, Jianming Zhao, and Wenquan Li.
2020. "Smart-Guided Pedestrian Emergency Evacuation in Slender-Shape Infrastructure with Digital Twin Simulations" *Sustainability* 12, no. 22: 9701.
https://doi.org/10.3390/su12229701