Network Models for Building Evacuation

Luc G. Chalmet · Richard L. Francis · Patsy B Saunders

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Evacuation and Crowd Dynamics Complexity and Algorithms in Graphs Facility Location and Emergency Management

Abstract

How can a large building with many occupants be evacuated in minimum time, and where are bottlenecks likely to occur in such an evacuation? In order to address this question we have constructed a family of three network building evacuation models. The most general model of interest, called the dynamic model, represents the evacuation of a building as it evolves over time, where time is represented discretely by consecutive time periods. The dynamic model triply optimizes in the sense that while directly minimizing the average over the occupants of the number of periods each needs to exit the building, it simultaneously maximizes the total number of people evacuating the building during periods 1 through p for all values of p, and also minimizes the time period in which the last evacuee exits the building. Coincident with the triple optimization, each arc dual variable indicates whether or not the building component the arc represents is a bottleneck in any period during the evacuation. The other two models in the family, referred to as the graphical model and the intermediate model, are smaller in scope than the dynamic model (they treat time as a parameter and are not time-dependent) but are easier to use, and offer alternative approaches which can provide some of the same insights as the dynamic model. We model the evacuation of an actual eleven floor building with 323 people, four elevators, and two stairwells, and compare model results with results of an observed building evacuation. We believe our models provide useful new tools for the analysis of building evacuability, and have the potential to facilitate the study of the interrelationships with building design, building redesign, and building evacuability.

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