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 traffic flow models for networks and related topics. 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 issues and present techniques to address those problems. Furthermore, we derive an adjoint calculus for scalar hyperbolic equations with nonlinear boundary control. The derived concepts fit for general network problems as well as they did for traffic flow issues. The principles of modeling and simplification can be applied to all kinds of network flows. Examples for applications are fluid flow in open channels or gas networks


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    Title :

    Mathematics of traffic flow networks : modeling, simulation and optimization


    Contributors:

    Publication date :

    2004


    Size :

    V, 134 S


    Remarks:

    21 cm
    graph. Darst



    Type of media :

    Theses


    Type of material :

    Print


    Language :

    English



    Classification :

    MSC:    35B37 / *90B20 / 76N15 / 35L65
    BKL:    31.76 Numerische Mathematik / 55.80 Verkehrswesen, Transportwesen: Allgemeines / 31.80 Angewandte Mathematik
    DDC:    510 / 380



    FINITE ELEMENT MODELING AND OPTIMIZATION OF TRAFFIC FLOW NETWORKS

    Mohr, G. A. | Taylor & Francis Verlag | 2005



    Modeling the Propagation of Traffic Flow Perturbations with Simple Mathematics

    Del Castillo, J. M. | British Library Conference Proceedings | 1998


    Optimization of traffic flow networks

    Kirchner, Claus | Tema Archive | 2007