New Models for Crowd Dynamics and Control

Abstract

In recent years, there has been an increasing interest in modeling crowd and evacuation dynamics. Pedestrian models are based on macroscopic or microscopic behavior. In this work, we are interested in developing models that can be used for evacuation control strategies. Hence, we use macroscopic modeling approach, where pedestrians are treated in an aggregate way and detailed interactions are overlooked. In this dissertation, we developed two-dimensional space crowd dynamic models to allow bi-directional low by modifying and enhancing various features of existing traffic and fluid dynamic models. In this work, four models based on continuum theory are developed, and conservation laws such as the continuity and momentum equations are used. The first model uses a single hyperbolic partial differential equation with a velocity-density relationship, while the other three models are systems of hyperbolic partial differential equations. For one of the system models presented, we show how it can be derived independently from a microscopic crowd model. The models are nonlinear, time-varying, hyperbolic partial differential equations, and the numerical simulation results given for the four macroscopic models were based on computational fluid dynamics schemes.

We also started an initial control design that synthesizes the feedback linearization method for the one-dimensional traffic flow problem applied directly on the distributed parameter system. In addition, we suggest and discuss the information technology requirements for an evacuation system.

This research was supported in part from the National Science Foundation through grant no. CMS-0428196 with Dr. S. C. Liu as the Program Director. This support is gratefully acknowledged. Any opinion, findings, and conclusions or recommendations expressed in this study are those of the writer and do not necessarily reflect the views of the National Science Foundation.