Modeling Exit Choice Behavior and Analyzing Information Influence in Crowd Evacuation

Modeling Exit Choice Behavior and Analyzing Information Influence in Crowd Evacuation

Problem Description

In emergency evacuation scenarios, an individual's exit choice behavior directly impacts the overall evacuation efficiency. Exit selection is influenced not only by physical distance but also by environmental information (such as congestion levels, smoke diffusion), social information (such as others' behaviors), and guidance information (such as broadcast instructions). Quantifying the impact of these factors on individual decision-making and predicting evacuation dynamics at the group level are key issues for optimizing evacuation strategies.

Key Knowledge Points and Step-by-Step Analysis

1. Basic Model: Limitations of the Nearest Exit Assumption

  • Traditional Assumption: Individuals default to choosing the geometrically nearest exit.
  • Limitations: In reality, individuals may abandon the nearest exit for the following reasons:
    • Congestion Perception: Observing high pedestrian density at the target exit, leading to a switch to another exit.
    • Information Asymmetry: Some individuals possess critical information (e.g., fire location) and actively avoid dangerous paths.
    • Herd Behavior: Following the flow of the majority, even if the path is longer.

2. Individual Decision-Making Model Framework

Exit choice can be modeled as a multi-attribute utility function, comprehensively evaluating the "attractiveness" of each exit:

\[U_i(j) = w_1 \cdot D_{ij} + w_2 \cdot C_j(t) + w_3 \cdot I_j + \epsilon \]

  • \(D_{ij}\): Distance from individual \(i\) to exit \(j\) (a negative indicator; shorter distance yields higher utility).
  • \(C_j(t)\): Congestion level at exit \(j\) at time \(t\) (e.g., number of people queuing).
  • \(I_j\): External information (e.g., reliability of guidance signs or hazard warnings).
  • \(w_1, w_2, w_3\): Weight parameters reflecting an individual's sensitivity to different factors.
  • \(\epsilon\): Random error term, representing unmodeled individual preferences.

3. Quantification Methods for Information Influence

  • Direct Information (e.g., broadcast guidance):
    • If an individual trusts the information, the \(I_j\) value for the target exit increases significantly.
    • Example: A broadcast announcing "Exit A is safe" increases \(I_A\) and the weight \(w_3\).
  • Indirect Information (e.g., observing others' behavior):
    • Herd Effect: Individuals tend to choose exits with high pedestrian density (even if farther away), which can be simulated by dynamically adjusting the weight of \(C_j(t)\).
    • Panic Contagion: Observing others running in a certain direction may trigger following behavior, requiring the addition of a social force term in the model.

4. Dynamic Updates and Path Correction

Individuals continuously perceive their environment and adjust decisions while moving:

  • Periodic Evaluation: Recalculate the utility of each exit at intervals of \(\Delta t\).
  • Trigger Conditions:
    • Increased congestion at the original target exit (\(C_j(t)\) rises), potentially triggering a switch.
    • Receipt of new information (e.g., smoke spreading to the current path), leading to a re-evaluation of \(I_j\).
  • Path Correction Cost: Considering inertia against switching (e.g., reluctance to turn back), add a switching penalty term to the utility function.

5. Group-Level Impact Analysis

  • Information Diffusion Range: When only some individuals receive guidance information, it is necessary to simulate the information diffusion network (e.g., proximity-based spread or mobile notifications).
  • Critical Proportion Effect: When the proportion of individuals receiving guidance reaches a threshold, overall evacuation efficiency improves significantly (e.g., reduced cross-flow conflicts).
  • Misinformation Risk: Incorrect information may cause crowds to gather at suboptimal exits. Introduce an information reliability factor \(\rho\) (\(0 \leq \rho \leq 1\)) into the model to adjust the actual impact of \(I_j\).

Example Demonstration

Assume a room with two exits (A and B) and an initially evenly distributed crowd:

  1. Baseline Scenario: Individuals choose exits based solely on distance. Result: Exit A (closer) quickly becomes congested, prolonging evacuation time.
  2. Incorporating Congestion Perception: Individuals adjust choices based on real-time congestion levels. Some switch to Exit B, reducing total evacuation time by 15%.
  3. Introducing Guidance Information: A broadcast announces "Exit B is safer," but only 30% of individuals trust this information. Simulation shows:
    • If the information is correct (Exit B is not dangerous), evacuation time further decreases by 10%.
    • If the information is incorrect (Exit B is actually more dangerous), evacuation time increases by 20%.

Summary

Modeling exit choice behavior requires integrating individual decision-making psychology, information dynamics, and group interactions. Through parameter calibration (e.g., weights \(w\) and information reliability \(\rho\)), the model can be applied to develop differentiated guidance strategies, such as:

  • Prioritizing sending guidance information to individuals in key locations to amplify influence through herd effects.
  • Dynamically adjusting information content (e.g., real-time updates on exit congestion) to avoid misinformation.