Math Modeling Contest: Optimized Plan to Leave the Louvre

Abstract

The distances between every section of the Louvre, exiting speeds dependent upon an individual's surroundings, time of day, total people, distribution of people, and stair dimensions are all factors utilized to establish a model for evacuating the Louvre. Our goal was to create an emergency protocol procedure that minimized the amount of time required to safely remove all guests from the Louvre. Using Dijkstra’s Algorithm to find the shortest path based on average distance between connecting nodes, three different piecewise difference equations were created to model the flow of guests out of the Louvre. With an average of 15,000 people touring the museum daily, we created an algorithm to distribute people based on time and section popularity for our initial conditions. Model One was the simplest, it had guests exit according to the shortest distance. Model Two was a bit faster as rerouted those who were outside of a node through a different exit pathway. Model Three was the fastest with a time of only 20 minutes until all guests had been successfully evacuated. With each model the bottlenecks were reduced. We suggest installing our Model Three emergency evacuation procedure within the Louvre's app. Once triggered, this model would guide all guests to the quickest exit pathways through the language selected by the user. Personnel would also be notified of were they should be stationed to help coordinate exit efforts at the high density nodes.