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A Fluid-Dynamic Traffic Model on Road Networks

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Abstract

We consider a mathematical model for fluid-dynamic flows on networks which is based on conservation laws. Road networks are studied as graphs composed by arcs that meet at some nodes, corresponding to junctions, which play a key-role. Indeed interactions occur at junctions and there the problem is underdetermined. The approximation of scalar conservation laws along arcs is carried out by using conservative methods, such as the classical Godunov scheme and the more recent discrete velocities kinetic schemes with the use of suitable boundary conditions at junctions. Riemann problems are solved by means of a simulation algorithm which processes each junction. We present the algorithm and its application to some simple test cases and to portions of urban network.

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Authors and Affiliations

  1. Department of Information Engineering and Applied Mathematics, University of Salerno, via Ponte don Melillo, 84084, Fisciano (SA), Italy

    Gabriella Bretti

  2. Istituto per le Applicazioni del Calcolo “M. Picone”, Viale del Policlinico 137, 00161, Rome, Italy

    Roberto Natalini & Benedetto Piccoli

Authors
  1. Gabriella Bretti
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  2. Roberto Natalini
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  3. Benedetto Piccoli
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Correspondence to Gabriella Bretti.

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Bretti, G., Natalini, R. & Piccoli, B. A Fluid-Dynamic Traffic Model on Road Networks. Arch Computat Methods Eng 14, 139–172 (2007). https://doi.org/10.1007/s11831-007-9004-8

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  • DOI: https://doi.org/10.1007/s11831-007-9004-8

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