Modeling Group Heterogeneity and Designing Differentiated Strategies in Emergency Evacuations

Topic Description
During emergency evacuations, crowds are not homogeneous groups but exhibit significant heterogeneous characteristics, such as differences in age, mobility, familiarity with the environment, and decision-making patterns. Group heterogeneity modeling aims to quantitatively analyze how these differences affect individual and group evacuation behavior and efficiency. Differentiated strategy design, based on the results of model analysis, involves developing guidance, resource allocation, or path planning schemes targeted at different subgroups to enhance the overall safety and efficiency of the evacuation. This topic will systematically explain how to mathematically describe and behaviorally model group heterogeneity, and on this basis, design effective differentiated evacuation strategies.

Explanation of the Problem-Solving Process

Step 1: Identify and Classify Key Heterogeneity Dimensions
First, it is necessary to clarify the key individual difference dimensions that affect evacuation behavior. Common dimensions include:

1. Physical Capabilities: Age (elderly, children), health status (disabled, injured), movement speed (fast, medium, slow).
2. Cognitive Abilities: Familiarity with the environment (familiar, unfamiliar), risk perception ability (calm, panicked), information processing ability.
3. Social Attributes: Whether part of a group (family, team), role within the group (guide, parent).
4. Behavioral Patterns: Decision-making style (rational calculation, following the crowd, habitual path dependence).

• Detailed Explanation: This step is the foundation of modeling. For example, differences in movement speed directly affect individual flow in corridors; familiarity with the environment influences an individual's confidence and efficiency in choosing paths—familiar individuals may know shortcuts, while unfamiliar ones are more prone to hesitation or following the crowd. These dimensions are not isolated; an individual may possess multiple heterogeneous characteristics simultaneously (e.g., an elderly person who moves slowly and is unfamiliar with the environment).

Step 2: Develop Parametric Models for Each Dimension
Transform the identified dimensions into quantifiable model parameters for computer simulation or mathematical analysis.

1. Parameterizing Mobility: Typically represented by a desired speed distribution. For example, divide the population into three groups: high-speed group (e.g., 1.5 m/s), medium-speed group (1.1 m/s), low-speed group (0.7 m/s), and assign a speed value to each individual.
2. Parameterizing Familiarity: Assign a "familiarity" weight (between 0 and 1) to each individual. Individuals with high familiarity (close to 1) rely more on their own knowledge when choosing paths, tending to select the shortest path; individuals with low familiarity (close to 0) rely more on following visible crowds or signs.
3. Parameterizing Decision Behavior: Agent-Based Models (ABM) can be used. For example, define an individual's decision rule: Path Selection Probability = Familiarity * (Shortest Path Attractiveness) + (1 - Familiarity) * (Herding Effect Strength).

• Detailed Explanation: Parameterization is the process of turning abstract characteristics into concrete numbers or rules, which is key to building a computable model. By setting different parameter values, we can simulate a wide variety of pedestrian individuals, thereby reproducing the complexity of real crowds in a computer.

Step 3: Construct an Evacuation Simulation Model Integrating Heterogeneity
Place the parameterized individuals into a simulated environment (e.g., a building floor plan with rooms, corridors, and exits). Commonly used models include extended versions of the social force model or cellular automaton models.

1. Model Initialization: At the start of the simulation, distribute individuals with different parameter combinations randomly or in specified areas. For example, out of 100 pedestrians, 20% are low-speed elderly, 30% are unfamiliar visitors (low familiarity).
2. Dynamic Interaction Simulation: During model runtime, each individual interacts in real-time with the environment (walls, exit distance) and other individuals (congestion, herding) based on their own parameters (speed, decision rules). Low-speed individuals may be overtaken by those behind, potentially forming bottlenecks; highly familiar individuals may choose less-used exits, thereby diverting flow.

• Detailed Explanation: Simulation is our core analysis tool. By running a large number of simulations, we can observe how heterogeneity leads to certain "emergent phenomena." For example, even a few low-speed individuals can cause temporary blockages at exits; the gathering of unfamiliar visitors may lead to overcrowding at main exits while underutilizing secondary exits.

Step 4: Analyze Simulation Results to Identify Key Issues
Analyze based on simulation output data (e.g., total evacuation time, exit utilization rate, crowd density heatmaps, trajectories of specific groups).

1. Bottleneck Analysis: Identify locations where high-density congestion persistently occurs during evacuation due to group heterogeneity. For example, analyze whether stairwell efficiency decreases due to mixing high-speed and low-speed individuals.
2. Group Difference Analysis: Compare the evacuation performance of different subgroups. For example, calculate whether the average evacuation time for the "unfamiliar visitor group" is significantly longer than that for the "familiar employee group."
3. Sensitivity Analysis: Change the distribution of heterogeneity parameters (e.g., increase the proportion of low-speed individuals) and observe how the total evacuation time changes to identify the most sensitive influencing factors.

• Detailed Explanation: This step is the process from "phenomenon" to "insight." Simulation is for identifying problems. For instance, analysis might reveal: "The problem is not the total number of people, but the most severe efficiency loss occurs when groups with large mobility differences mix in narrow spaces."

Step 5: Design and Evaluate Differentiated Strategies
Based on the problems identified in the previous step, design strategies targeted at different subgroups and evaluate their effectiveness through simulation again.

1. Targeted Guidance Strategies:
   • For Unfamiliar Visitors: Install more prominent and dense guidance signs or audio broadcasts at key decision points to compensate for their cognitive shortcomings.
   • For Low-Speed Groups (elderly, disabled): Preset priority passages or refuge areas to avoid intersection with the main flow; or arrange staff assistance for phased evacuation.
2. Spatial and Facility Optimization:
   • Install handrails or widen passages in bottleneck areas (e.g., stairwell entrances) to reduce conflicts arising from speed differences.
   • Set up "Dedicated Knowledgeable Exits" for highly familiar groups and clearly mark them to guide their diversion, relieving pressure on main exits.
3. Differentiated Information Dissemination: Send customized information to different groups via mobile apps or broadcasts. For example, notify familiar employees to use secondary exits while guiding visitors to evacuate along the main route.

• Detailed Explanation: The core of strategy design is "targeting the root cause." The effectiveness of differentiated strategies must be verified by returning to Step 3 and incorporating the strategy rules into the simulation model. For example, set a priority path for the "low-speed group" in the model and then compare the total evacuation time and that group's evacuation time before and after strategy implementation, using data to prove the strategy's effectiveness. An optimized strategy should improve overall system efficiency while ensuring the safety of vulnerable groups.

Through the above five steps, we have completed the entire process from identifying group differences, to modeling and analyzing their impact, to ultimately designing and verifying targeted strategies. This approach elevates evacuation planning from a "one-size-fits-all" crude model to a refined and humanized level.