Dynamic Evolution and Role Transition Mechanisms of Leader-Follower Dynamics in Crowd Evacuation

Dynamic Evolution and Role Transition Mechanisms of Leader-Follower Dynamics in Crowd Evacuation

Problem Description

In emergency evacuation scenarios, individual roles are not fixed. Some initially passive followers may spontaneously transition into temporary leaders within a dynamic environment, while original leaders may lose influence due to decision-making errors or physical exhaustion. This problem requires analyzing the dynamic evolution mechanisms of leader and follower roles, including the triggering conditions for role transitions, the impact of the transition process on group evacuation efficiency, and how to model such behavior.

Detailed Solution Steps

Step 1: Clarify Role Definitions and Transition Types

Leader: An individual who actively guides others and assumes responsibility for path exploration or decision-making during evacuation, typically possessing higher risk perception, sense of direction, or physical stamina.
Follower: An individual who relies on others' guidance and tends to conform to the group.
Role Transition Types include:

  • Follower → Leader: Occurs when the original path is blocked, the leader becomes incapacitated, or an individual discovers a more optimal path.
  • Leader → Follower: Occurs when the leader's decision is proven wrong, physical stamina is insufficient, or a more authoritative competitor emerges.

Step 2: Analyze Triggering Conditions for Role Transitions

  1. Environmental Pressure Changes:
    • When risks escalate, such as exit congestion or smoke diffusion, some followers may actively seek alternatives, triggering role transitions.
    • Quantify environmental pressure through local density threshold (e.g., per capita space below 0.5 m²) or danger perception function (e.g., decreasing distance to a fire source).
  2. Dynamic Social Influence:
    • An individual's trust in a leader is updated in real-time based on decision outcomes. If the time taken on a path guided by the leader exceeds expectations, followers may reduce their influence weight, which can be expressed by the formula:

\[ Trust_{i}(t) = Trust_{i}(t-1) - \alpha \cdot (ActualTime - ExpectedTime) \]

 where $\alpha$ is the trust decay coefficient.
  1. Individual Trait Differences:
    • Individuals with high risk-taking propensity, familiarity with the environment, or ample physical stamina are more likely to transition into leaders. It is necessary to introduce personality parameters (e.g., risk-taking coefficient \(β \in [0,1]\)) and knowledge level parameters (e.g., environmental familiarity \(γ\)).

Step 3: Establish a Dynamic Role Transition Model

  1. State Monitoring Module:
    • Track in real-time each individual's position, speed, decision history, and surrounding density.
    • For example, judge the effectiveness of the current path by the average movement speed within the perception radius: if the speed consistently falls below a threshold \(v_{min}\), trigger a re-evaluation.
  2. Transition Probability Calculation:
    • Based on logistic regression or random utility theory, define the probability of follower \(i\) transitioning to a leader at time \(t\):

\[ P_{i}(t) = \frac{1}{1 + e^{-(k_1 \cdot RiskExposure + k_2 \cdot β_i + k_3 \cdot γ_i)}} \]

 where $k_1, k_2, k_3$ are weight parameters, and $RiskExposure$ is determined by both distance to the danger source and local density.
  1. Leader Authority Competition Mechanism:
    • If multiple individuals simultaneously attempt to assume the leader role, employ authority value competition:

\[ Authority_j = Trust_j \cdot (1 + δ \cdot Experience_j) \]

 The individual with the highest authority value becomes the actual leader, while others revert to follower status or form sub-groups.

Step 4: Evaluate the Impact of Role Transitions on Evacuation Efficiency

  1. Positive Effects:
    • Multiple leaders can split the group, reducing pressure on single exits and avoiding global congestion caused by the "herd effect."
    • Quantify evaluation using metrics like split ratio (number of sub-groups / total population) and average evacuation time.
  2. Negative Effects:
    • Frequent role transitions may lead to decision oscillations, increasing group chaos.
    • Introduce a chaos index (e.g., variance of individual direction change frequency) to measure stability.

Step 5: Simulation Verification and Parameter Calibration

  • Build a multi-agent model in platforms like NetLogo or AnyLogic, setting different initial leader ratios and environmental complexity scenarios.
  • Adjust triggering condition parameters (e.g., density threshold, trust decay coefficient) through sensitivity analysis to observe trends in evacuation time and survival rate.

Key Knowledge Points Summary

  • Role transition is a manifestation of group adaptability and requires dynamic modeling that combines environmental stimuli and individual traits.
  • The model must balance the efficiency gains from leader diversity against the risk of decision-making chaos.
  • In practical applications, wearable devices can monitor individual states (e.g., a sudden spike in heart rate indicating stress-triggered role transition) to provide data support for intelligent guidance systems.