# Cynicicm/American-mathematical-modeling

2019美国大学生数学建模大赛论文
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# American-mathematical-modeling

## 2019美国大学生数学建模大赛

### Time to leave the Louvre

#### Abstract

In this paper, we make a series of explorations on the design of the Louvre emergency evacuation plan,and construct a comprehensive revenue model and an equilibrium flow model based on cellular automatafor the evacuation of the ground floor and the evacuation between floors. Finally, pathfinder software is applied to simulate and verify the optimal paths of the model solution.

We first consider that the evacuation is evacuated from the building process, define the comprehensive benefit as the principle of ideal choice evacuation of personnel evacuation path, based on cellular automata thought, set the maximum comprehensive benefit grid for the direction of the cellular state transition, which based on cellular automata evacuation path model of comprehensive income.

For the selection of evacuation path between floors, an equilibrium flow model is constructed to balance the flow of people in different paths and realize the reasonable distribution of people in public sections, so as to reduce the degree of evacuation congestion and evacuation time.

Cellular automata simulation by matlab to explore the influence of different factors on the evacuation rules, which determine the gain coefficient of different evacuation situation of optimal value range, using the three-dimensional evacuation simulation software pathfinder to various circumstances evacuation path for simulation model, and compared with the short circuit model to determine the evacuation route, found that the present model to determine the evacuation efficiency of path is optimal; In addition, a three-dimensional model of the Louvre is built by pathfinder, and the corresponding evacuation paths are obtained through simulation.

Finally, the models are evaluated and generalized, and the policy and procedural recommendations for Louvre emergency management are given based on the research conclusions of this paper.

Key Words : Emergency evacuation; Comprehensive income; Cellular Automata; Equilibrium flow;Pathfinder simulation

### 离开卢浮宫的时间到了

#### 摘要

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