Time Estimation and Dynamic Adjustment in Emergency Evacuation

Time Estimation and Dynamic Adjustment in Emergency Evacuation

Problem Description
The core of time estimation and dynamic adjustment in emergency evacuation is to study how to accurately predict the total time required for a crowd to completely evacuate from a hazardous area (Required Safe Egress Time, RSET), and to dynamically adjust the estimated time and evacuation strategy when the process deviates from expectations due to environmental changes (such as fire spread, passage blockages) or fluctuations in crowd behavior. The difficulty lies in that time estimation requires comprehensive consideration of multiple factors such as physical space, crowd density, and movement speed, while dynamic adjustment demands that the system possesses real-time monitoring and feedback capabilities.

Step-by-Step Explanation of the Solution Process

Step 1: Understanding Basic Concepts – The Composition of Evacuation Time
Total evacuation time (RSET) is not a single value; it is the sum of several key time periods:

  1. Detection Time: The time from the onset of a hazard (e.g., fire) until it is identified by a detection system (e.g., smoke detector).
  2. Alarm Time: The delay from system detection to issuing an alarm to the crowd.
  3. Pre-movement Time: The time spent by the crowd after receiving the alarm, before starting to move, on activities such as confirming information, gathering belongings, notifying others, etc. This phase is most variable and heavily influenced by crowd psychology.
  4. Movement Time: The time required for the crowd to physically move from their starting positions to a safe location.
  • Key Point: Accurate time estimation must estimate these four stages separately, especially the pre-movement time. One cannot simply assume the crowd will start moving immediately.

Step 2: Building a Static Time Estimation Model
Perform an initial estimation before the evacuation begins, based on known conditions. A common method is the Hydraulic Analogy Model (e.g., queuing model):

  1. Calculate Movement Time:
    • Identify the Critical Path: Find the route from the farthest location to the safe exit. This path often determines the total movement time.
    • Analyze Bottlenecks: Identify narrow points along the path (e.g., doors, stairs) and calculate their capacity (number of people that can pass per unit time). For example, a 1-meter-wide door has a flow rate of approximately 60 people/minute.
    • Apply Formulas: Total movement time ≈ (Total number of people / Minimum bottleneck flow rate) + (Farthest distance / Average crowd movement speed).
    • Simplified Example: A room has 100 people, the narrowest door can pass 30 people/minute, the farthest person is 50 meters from the door, and the average crowd speed is 1 m/s. Then movement time ≈ (100 people / 30 people/minute) + (50 meters / 1 m/s) ≈ 3.33 minutes + 50 seconds ≈ 4.2 minutes.
  2. Add Other Times: Add the estimated detection time, alarm time, and pre-movement time (which can be set as a range based on historical data or behavioral studies, e.g., 2-5 minutes) to the movement time to obtain the initial RSET estimate.

Step 3: Introducing Dynamic Factors and Real-Time Monitoring
The static estimate is a baseline under ideal conditions. In reality, the situation changes, requiring dynamic adjustment. This necessitates establishing a Monitoring-Feedback-Adjustment Loop:

  1. Real-Time Data Collection:
    • Environmental Monitoring: Use sensors to monitor fire spread speed, temperature, smoke concentration, etc. These factors can block paths or force route changes.
    • Crowd Monitoring: Track crowd density, flow speed, and congestion points in real-time via cameras or IoT devices. For example, detecting that movement speed in a stairwell is far below expectations (e.g., dropping from 1 m/s to 0.2 m/s).
  2. Comparison and Early Warning:
    • Compare the real-time monitored progress of crowd movement (e.g., "30% of people have reached the safe zone") with the progress timeline predicted by the static model.
    • If the actual progress lags significantly behind the prediction (e.g., 50% predicted safe vs. 20% actual), trigger an early warning indicating the initial RSET estimate has become overly optimistic.

Step 4: Executing Dynamic Time Adjustment and Strategy Optimization
When the monitoring system issues a warning, the system initiates dynamic adjustment instead of relying on the initial static RSET:

  1. Re-estimate RSET:
    • Recalculate based on real-time data from the current moment. For example, finding that the main stairwell is congested, reducing its effective capacity from 60 people/minute to 20 people/minute.
    • New movement time = (Number of people not yet evacuated / Current actual bottleneck flow rate) + (Remaining farthest distance / Current average speed).
    • Combine the new movement time with the remaining pre-movement time (some people may not have started moving) to derive an updated, more realistic RSET. This new time is typically longer than the initial estimate.
  2. Adjust Evacuation Strategy:
    • Path Re-allocation: If the system detects severe congestion at Exit A but underutilization of Exit B, it can guide part of the crowd to Exit B via dynamic signage or broadcasts.
    • Phased Evacuation: In high-rise buildings, evacuate floors directly threatened first, while delaying evacuation of other floors to prevent fatal congestion in stairwells.
    • Information Intervention: Send more urgent and specific instructions to people still in the pre-movement phase (e.g., "Please abandon belongings immediately and evacuate via the west stairwell") to shorten their remaining pre-movement time.

Summary
Time estimation and dynamic adjustment in emergency evacuation is a process from "static planning" to "dynamic management." The core lies in recognizing that time estimation is not a one-time task but a dynamic variable that needs continuous revision based on real-time feedback. A robust evacuation system must integrate real-time monitoring, rapid data analysis capabilities, and flexible command strategies to maximize personnel safety in the rapidly changing circumstances of an emergency.