Features

• Presents the derivation of conservation laws for mass, momentum, and energy
• Covers one-dimensional macroscopic traffic models and systems of relaxation PDE models
• Introduces traffic models that allow for distributed control via the traffic flux term and modeling of one- and two-dimensional traffic
• Includes the necessary background mathematical theory for scalar conservation laws and relaxation models
• Examines the existence results for optimal time and cost controls for traffic control problems
• Tabulates closed-loop behaviors of physical interest arising from various specific choices of feedback control laws
• Discusses numerical simulations using Godunov’s method for advective control problems for initial-boundary data problems

Summary

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.