Exit Capacity and Bottleneck Analysis in Crowd Evacuation

Exit Capacity and Bottleneck Analysis in Crowd Evacuation

Problem Description
In crowd evacuation scenarios, exit capacity and bottleneck analysis are key to optimizing evacuation efficiency. Exit capacity refers to the maximum number of people that can pass through an exit per unit of time, while bottlenecks refer to critical nodes that restrict the overall flow rate (such as narrow passages, stairs, doors, etc.). The problem requires analyzing how to quantify exit capacity, identify bottlenecks, and formulate strategies to alleviate congestion, thereby shortening evacuation time.

Solution Process

1. Understanding Factors Influencing Exit Capacity

  • Physical Width: The physical width of an exit directly determines the number of people who can pass through simultaneously. For example, a standard door (0.9 meters wide) can allow approximately 30-40 people per minute to pass, while a 2-meter-wide exit can allow about 80-100 people.
  • Flow Speed: Crowd density affects movement speed. At high density (e.g., 6 people/square meter), speed drops to 0.3-0.5 meters/second; at low density (2 people/square meter), it can reach 1.2 meters/second.
  • Psychological and Behavioral Factors: Panic may lead to congestion, pushing, or herd behavior, further reducing actual capacity.

2. Calculating Exit Capacity

  • Basic Formula: Exit capacity \(C\) (people/minute) can be approximated as:

\[ C = W \times v \times \rho \]

where:

  • \(W\) = Effective exit width (meters)
  • \(v\) = Crowd flow speed (meters/second)
  • \(\rho\) = Crowd density (people/square meter)
  • Example: Assuming an exit width of 1.5 meters, a density of 4 people/square meter, and a speed of 0.8 meters/second, then:

\[ C = 1.5 \times 0.8 \times 4 \times 60 = 288 \ \text{people/minute} \]

Note: In practice, a safety factor must be considered, typically 70%-80% of the theoretical value.

3. Identifying Bottlenecks

  • Bottleneck Characteristics:
    • Flow rate is lower than upstream input (e.g., crowd accumulation at a stair entrance).
    • Sudden changes in physical structure (e.g., a wide passage connecting to a narrow door).
    • Utilization of critical nodes is close to 100%.
  • Analysis Methods:
    • Dynamic Simulation: Use software (e.g., AnyLogic, FDS+Evac) to simulate crowd flow and observe congestion points.
    • Field Observation: Record the passage time at each node during evacuation drills and compare it with theoretical capacity.

4. Strategies to Alleviate Bottlenecks

  • Increase Parallel Exits: Open backup exits or temporarily widen passages (e.g., by removing obstacles).
  • Flow Control and Diversion:
    • Guide people to idle exits using guides or signage.
    • Use barriers to form one-way flow and reduce counterflow.
  • Timing Optimization:
    • Conduct evacuation in batches (e.g., delayed start by floor in high-rise buildings) to avoid peak congestion.
    • Use broadcast systems to adjust evacuation rhythm in real-time.

5. Verification and Iteration

  • Post-Evaluation: Compare evacuation times before and after strategy implementation to calculate improvement.
  • Sensitivity Analysis: Test capacity changes under different density and speed assumptions to ensure strategy robustness.

Through the above steps, evacuation efficiency can be systematically optimized, reducing the impact of bottlenecks on safety.