Pedestrian Dynamics : Mathematical Theory and Evacuation Control book cover
1st Edition

Pedestrian Dynamics
Mathematical Theory and Evacuation Control

  • This format is currently out of stock.
ISBN 9781439805190
Published March 24, 2009 by CRC Press
169 Pages 65 B/W Illustrations

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Book Description

Homeland security, transportation, and city planning depend upon well-designed evacuation routes. You can’t wait until the day of to realize your plan won’t work. Designing successful evacuation plans requires an in-depth understanding of models and control designs for the problems of traffic flow, construction and road closures, and the intangible human factors. Pedestrian Dynamics: Mathematical Theory and Evacuation Control clearly delineates the derivation of mathematical models for pedestrian dynamics and how to use them to design feedback controls for evacuations.

The book includes:

  • Mathematical models derived from basic principles
  • Mathematical analysis of the model
  • Details of past work
  • MATLAB® code
  • 65 figures and 400 equations

Unlike most works on traffic flow, this book examines the development of optimal methods to effectively control and improve pedestrian traffic flow. The work of a leading expert, it examines the differential equations applied to conservation laws encountered in the study of pedestrian dynamics and evacuation control problem. The author presents new pedestrian traffic models for multi-directional flow in two dimensions. He considers a range of control models in various simulations, including relaxed models and those concerned with direction and magnitude velocity commands. He also addresses questions of time, cost, and scalability. The book clearly demonstrates what the future challenges are and provides the tools to meet them.

Table of Contents



Literature Survey


Derivation of Conservation Laws

Mass Conservation

Momentum Conservation

Energy Conservation

Combined Equations

General Conservation

Traffic Models: One Dimensional Case

Lighthill-Whitham-Richards Model

Payne-Whitham Model

Aw-Rascle Model

Zhang Model

Pedestrian and Control Models in One Dimension

Traffic Models: Two-Dimensional Case

Two-Dimensional LWR Model

Two-Dimensional Payne-Whitham Model

Two-Dimensional Aw-Rascle Model

Two-Dimensional Zhang Model

Conservation Law Solutions

Method of Characteristics

Classical or Strong Solutions

Weak Solutions

Scalar Riemann Problem

Admissibility Conditions

Kruzkov’s Entropy Function


Oleinik Entropy Condition

Scalar Initial-Boundary Problem

Traffic Control

Scalar Conservation Law Solution

Dynamical Systems and C0-Semigroups

Optimal Control

Optimal Flux Control for Scalar Conservation Law

Feedback Control for Scalar Law

Advective Feedback Control for Relaxation Systems

Wellposedness for Bounded Advection Control

Simulations for Advective Control

Godunov’s Method

Simulation Results for Advective Control




Future Work

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