#
HyPedSim: A Multi-Level Crowd-Simulation Framework—Methodology, Calibration, and Validation^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

- Strategic level: pedestrians determine a list of activities (or targets) and when they want to perform these activities.
- Tactical level: pedestrians choose a path to the predefined destinations based on information about the environment.
- Operational level: pedestrians adjust their local movements such as collision avoidance to adapt to the surrounding area.

^{2}[1]. These models encounter specific problems when applied to high-density situations, such as abnormal vibrations with the Social Force Model [10], congestion in dense bidirectional flow with the Velocity Obstacle Model [11], and unrealistic results in terms of collision metrics with the data-driven models [12,13]. On the other hand, pedestrian dynamics in high-density situations are similar to fluid flow [14], and fluid-like equation models [14,15] are particularly appropriate for these scenarios due to their assumption of the continuousness of pedestrian flow. Given the observed variability in the performance of pedestrian-simulation models across different crowd densities, the integration of multiple models is required to accommodate the full spectrum of potential scenarios.

## 2. Related Work

## 3. HyPedSim Framework

#### 3.1. General Overview

#### 3.2. Agent-Based Model for Multi-Level Behaviour

#### 3.3. Pedestrian Activity Diagram

## 4. Application to the Festival of Lights

#### 4.1. Festival of Lights

#### 4.2. Data Collection

#### 4.3. Pedestrian-Simulation Models

#### 4.3.1. Social Force Model

#### 4.3.2. Continuum Crowds Model

#### 4.3.3. Hybrid Model

**Specification of operational level models**: During the pedestrian exit process at the Place des Terreaux, the plaza experiences high density, while the two exit roads exhibit lower density. To handle these multi-density dynamics, the environment is divided into three distinct zones (as illustrated via the three rectangles in Figure 4). The plaza is specified as a high-density zone (red rectangle) and two exit roads are specified as low-density zones (blue rectangles). Each zone is characterised by one specific operational level model for pedestrian simulation. The specifications of the operational level models for these zones are as follows:

- The CC model [15] for a single target cell is used to simulate pedestrians in the high-density zone due to its effectiveness in dense scenarios. This approach leads to further discretisation into cells, each storing information about the environment and the pedestrians, such as average velocity and local density.
- The SFM [7] is applied to the two low-density zones to simulate pedestrians who have exited the plaza to one of the two exit roads, as it can realistically simulate pedestrians in low-density situations.

**Criteria to transition operational level models**: The transition criteria are activated as soon as pedestrian agents move out of the high-density zone into a new, low-density zone. When this occurs, the transition rule is applied, which sets the variable $operational\_level=SFM$. Additionally, the parameter ${t}_{delay}$ is introduced to provide better control over the transition by causing pedestrians to stand still for a short period after exiting the high-density zone.

**Exit choice behaviour**: Once pedestrians meet the transition criteria, they probabilistically select one of the two available exit roads. The probability of choosing an exit road depends on the distance to each of the exit roads at that time:

- If pedestrians are closer to Constantine Road, they choose Constantine Road as the exit road with the probability of $\alpha $ and Chenavard Road with the probability of $1-\alpha $.
- Conversely, if pedestrians are closer to Chenavard Road, they choose Chenavard Road as the exit road with the probability of $\beta $ and Constantine Road with the probability of $1-\beta $.

#### 4.4. Model Calibration

- Hybridisation: ${t}_{delay},\alpha ,\beta $.
- Parameters of SFM: $A,B,{V}^{pref},\tau $.
- Parameters of CC: ${f}_{min},{f}_{max},{\rho}_{min},{\rho}_{max}$.

**Initialisation**: A population of 128 individuals is initialised, with each individual representing a chromosome consisting of 11 genes corresponding to 11 parameters for calibration. Each parameter gene was initialised via random sampling from a defined range of minimum to maximum values specific to that parameter. The value interval of the parameters for each pedestrian-simulation model is chosen based on settings commonly used in the literature [7,15]. Let ${\varphi}_{i}$ denote the ith parameter gene in each chromosome, where ${\varphi}_{i}^{min}$ and ${\varphi}_{i}^{max}$ are the minimum and maximum allowable values of the parameter ${\varphi}_{i}$, respectively. Table 1 depicts the range of values for the parameters.**Fitness evaluation**: The fitness of individuals in the population is evaluated by comparing the simulated outflow data, extracted from simulations of a crowd exiting at the Festival of Lights, with observed outflow using the fitness function in Equation (8). A total of $N=20$ observations are selected via systematic sampling. Implementation details of the simulations are described in the next section.**Selection**: This process refers to choosing individuals with the best fitness values from the population to serve as parents for generating offspring for the next generation. In this work, 50% of individuals with the lowest fitness values in each generation are selected as parents for crossover and retained for the next generation.**Crossover**: Pairs of parent individuals in the best-selected set are combined to reproduce offspring. Uniform crossover is used with each gene of an offspring’s chromosome having a 0.5 probability of originating from the corresponding gene of either parent, as shown in Figure 8.**Mutation**: The mutation operator randomly alters chromosomes to prevent converging to a locally optimal solution. A mutation rate of 0.01 is applied to each gene in a chromosome. If a mutation occurs for the parameter gene ${\varphi}_{i}$:$${\varphi}_{i}={\varphi}_{i}^{min}+\gamma ({\varphi}_{i}^{max}-{\varphi}_{i}^{min}),\phantom{\rule{1.em}{0ex}}0\le \gamma \le 1.$$

#### 4.5. Simulation Details

- The simulation is conducted with a time step $\Delta t=0.1$ s, with 3883 agents.
- Pedestrians are initialised with a uniform distribution across the high-density zone.
- All simulations are conducted using the GAMA platform [30] on a M1 MacBook Pro with 32 GB of memory.

#### 4.6. Calibration Results

#### 4.7. Model Validation

#### 4.8. Sensitivity Analysis

## 5. Performance Analysis

- SFM-only model: the SFM is applied in all three zones.
- 3-CC-1 model: consists of three separate CC models, each with one target cell for simulating one single zone.
- 1-CC-2 model: one CC model for simulating the entire environment, with two designated target cells representing two exit roads. This configuration increases computational complexity compared to using only one target cell.

- Density map (in ped/m
^{2}) of pedestrian density distribution across the simulation area. - Computation time (in s) required to calculate one simulation step.

^{2}, is observed in both the plaza and the two exits. Similarly, the 3-CC-1 model and 1-CC-2 model can simulate extremely high densities of 6–8 ped/m

^{2}, but these extremely high-density areas also appear in both the plaza and the two exits. In contrast, the hybrid model exhibits a clear difference in density levels between the plaza and the two exits. These results indicate that the hybrid model can effectively simulate pedestrians in environments with a mix of low- and high-density situations. Furthermore, a key advantage of this model is its generic nature and flexibility, as it can accommodate any combination of zones and models, enabling the modelling of various scenarios and crowd dynamics.

## 6. Conclusions and Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

SFM | Social Force Model |

CC | Continuum Crowds |

GA | Genetic Algorithm |

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**Figure 4.**A screenshot of pedestrians watching the show at the Place des Terreaux in 2022 (https://www.fetedeslumieres.lyon.fr/fr/oeuvre/grand-mix-au-musee-des-beaux-arts-de-lyon (accessed on 30 January 2024)) and main circulation of the exiting crowd.

**Figure 5.**Empirical outflow of pedestrians. (

**a**) The outflow of Constantine Road. (

**b**) The outflow of Chenavard Road.

**Figure 11.**Comparison of observed and simulated outflow for the two exit roads. (

**a**) Constantine Road. (

**b**) Chenavard Road.

**Figure 12.**Local sensitivity analysis for different parameters. (

**a**) ${t}_{delay}$, (

**b**) $\alpha $, (

**c**) $\beta $, (

**d**) A, (

**e**) B, (

**f**) ${V}^{pref}$, (

**g**) $\tau $, (

**h**) ${f}_{min}$, (

**i**) ${f}_{max}$, (

**j**) ${\rho}_{min}$, (

**k**) ${\rho}_{max}$.

**Figure 14.**Simulation results. (

**a**) Simulation of 6000 agents at the Place des Terreaux using the hybrid model with pedestrians in the high-density zone in red and those in the low-density zones in blue. (

**b**) Comparison of performance for different models.

Type | Parameter ${\mathit{\varphi}}_{\mathit{i}}$ | ${\mathit{\varphi}}_{\mathit{i}}^{\mathbf{min}}$ | ${\mathit{\varphi}}_{\mathit{i}}^{\mathbf{max}}$ |
---|---|---|---|

Hybrid | ${t}_{delay}$ | 0.0 | 1.0 |

$\alpha $ | 0.0 | 1.0 | |

$\beta $ | 0.0 | 1.0 | |

SFM | A | 0.5 | 5.0 |

B | 0.1 | 0.5 | |

${V}^{pref}$ | 0.8 | 1.5 | |

$\tau $ | 0.4 | 0.6 | |

CC | ${f}_{min}$ | 0.05 | 0.25 |

${f}_{max}$ | 0.8 | 1.6 | |

${\rho}_{min}$ | 0.05 | 0.5 | |

${\rho}_{max}$ | 6.0 | 8.0 |

Parameter${\mathit{\varphi}}_{\mathit{i}}$ | ${t}_{delay}$ | $\alpha $ | $\beta $ | A | B | ${V}^{pref}$ | $\tau $ | ${f}_{min}$ | ${f}_{max}$ | ${\rho}_{min}$ | ${\rho}_{max}$ |

Best value | 0.9 | 0.91 | 0.76 | 1.83 | 0.45 | 1.25 | 0.57 | 0.15 | 1.35 | 0.11 | 6.36 |

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**MDPI and ACS Style**

Dang, H.-T.; Gaudou, B.; Verstaevel, N.
HyPedSim: A Multi-Level Crowd-Simulation Framework—Methodology, Calibration, and Validation. *Sensors* **2024**, *24*, 1639.
https://doi.org/10.3390/s24051639

**AMA Style**

Dang H-T, Gaudou B, Verstaevel N.
HyPedSim: A Multi-Level Crowd-Simulation Framework—Methodology, Calibration, and Validation. *Sensors*. 2024; 24(5):1639.
https://doi.org/10.3390/s24051639

**Chicago/Turabian Style**

Dang, Huu-Tu, Benoit Gaudou, and Nicolas Verstaevel.
2024. "HyPedSim: A Multi-Level Crowd-Simulation Framework—Methodology, Calibration, and Validation" *Sensors* 24, no. 5: 1639.
https://doi.org/10.3390/s24051639