## 3 Materials and Methods
Case 2: Introducing pre-evacuation delays and delays at intersections, with increasing error probability and variable miner speeds to examine the effect of stamina on the evacuation times. * Smart Evacuation: In the smart evacuation scenario, miners were guided by a smart device that eliminated human error by providing real-time, optimized escape routes. A real-time optimization algorithm continuously directed each miner to the safest, nearest shelter based on their current location, any path blockages, available routes, distance to shelters, and individual stamina levels. This guidance was updated dynamically for each person, addressing changing conditions underground. The optimization model underlying this process was designed to solve the minimum-cost network flow algorithm, ensuring that miners reached safety efficiently and with minimized evacuation time. This scenario also featured two cases: 1. Case 1: Introducing pre-evacuation delays; 2. Case 2: Operating without pre-evacuation delays. Both cases were run for miners with uniform and variable stamina, achieved through different speeds for each miner. * Passive Signage: In traditional underground mine evacuation scenarios, miners rely on passive signage to navigate toward safe exits. These signs are typically static indicators--such as arrows, illuminated signs, or color-coded paths--that mark designated escape routes. While passive signage is simple and cost-effective, it lacks the ability to adapt to real-time conditions like changing hazards, blocked pathways, or individual miner locations. Consequently, in emergencies with complex or evolving conditions, traditional signage may lead to delays or confusion as miners must interpret and follow predetermined routes that may no longer be optimal. Despite these limitations, passive signage remains a fundamental component of safety protocols and is often combined with training to ensure miners are familiar with evacuation routes. This scenario included the following: 1. Single Case: Keeping pre-evacuation delay constant while varying the delay at intersections and the error percentage. It was run for miners with both uniform and variable stamina, with differences in stamina achieved by varying speeds. To simplify the simulation model, some assumptions were made, including the following:  
* All miners had the same role. * There was no interaction between the miners and the environment. * Only wayfinding and pre-evacuation behaviors were considered. * Wayfinding and pre-evacuation behaviors were treated as delays. * All miners evacuated on foot. * All miners followed the evacuation plan in the smart evacuation scenario; however, their behavior may vary. * The evacuation time was defined as the time it took for the last miner to leave the mine. Validation. The last step of the proposed methodology was focused on validating the simulation results. The model's validation involved comparing simulated evacuation times against calculated times based on predefined miner speeds and the physical layout of the mine. This comparison helped confirm the accuracy of the simulation model in predicting realistic evacuation outcomes. The primary outcome measure was the evacuation time, with additional analysis focusing on the influence of individual and collective behaviors on the efficiency of different evacuation strategies. The study aimed to identify key factorsthat significantly impacted evacuation time and safety, informing the development of more effective evacuation protocols and training programs for mine safety.