Abstract
A mathematical model for the evacuation of people from a road tunnel is created, taking into account various factors such as the speed at which people move, the density of the flow of people, and the outcome of the fire. This model allows for the precise calculation of the evacuation time and the optimization of the evacuation route in a fire scenario. The constructed mathematical model was used to determine how long it would take for people to evacuate this road tunnel, and the findings of the Pathfinder simulation were compared. The findings demonstrate a relationship between the model's evacuation time and the human flow density, movement velocity, and fire product characteristics. The evacuation time is closer to the outcome of the actual fire scene when the impact of the fire environment on the speed of evacuation is quantified. The mathematical model of human evacuation's calculation of the evacuation time is essentially accurate when compared to the Pathfinder simulation's calculation, with an error of only 0.77 %. The model provides recommendations for optimizing the evacuation of people from a road tunnel in the case of a fire by not only predicting where the crowding would occur but also by calculating the duration of the crowding.