Mathematics of Traffic Flow Networks: Modeling, Simulation and Optimization

Herty, Michael

ISBN 10: 3832506187 / ISBN 13: 9783832506186

Published by Logos Verlag Berlin, 2004

About this Item

2004. paperback. . . . . . Books ship from the US and Ireland.

Seller Inventory # V9783832506186

Bibliographic Details

• Title: Mathematics of Traffic Flow Networks: Modeling, Simulation and Optimization
• Publisher: Logos Verlag Berlin
• Publication Date: 2004
• Language: English
• ISBN 10: 3832506187
• ISBN 13: 9783832506186
• Binding: Soft cover
• Condition: New

About this title

Synopsis

Traffic flow has been a continuous source of challenging mathematical problems. The following work is dedicated to recent questions in modeling, simulation and optimization of traffic flow networks. Mathematics can help to solve traffic problems in different ways. Modelling provides fundamental understanding of traffic dynamics and behaviour. Optimization yields solutions for complex situations and helps to organize traffic flow. During the last decade there has been intensive research in different fields of and related to traffic flow. One of the primary research activities focus on the development of new and more realistic models for traffic flow on a single road. Our work's primary focus is on models for networks. We provide new ideas on modelling flow in networks and solve different optimization problems analytically and numerically. The main result is the derivation of a hierarchy of models treating different situations with suitable traffic flow models. To each level of modeling we consider the optimal control problems and present techniques to address those problems. Furthermore, we derive an adjoint calculus for scalar hyperbolic equations with nonlinear boundary controls. The derived concepts fit for general network problems as well as they do for traffic flow issues. The principles of modeling and simplification can be applied to all kinds of network flows, like fluid flow in open channels or gas networks.