Numerical approximations of a traffic flow model on networks | Zendy

Gabriella Bretti | Zendy; Roberto Natalini | Zendy; Benedetto Piccoli | Zendy

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Numerical approximations of a traffic flow model on networks

Author(s) -

Gabriella Bretti,

Roberto Natalini,

Benedetto Piccoli

Publication year - 2006

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2006.1.57

Subject(s) - conservation law , riemann problem , godunov's scheme , scalar (mathematics) , computer science , mathematics , simple (philosophy) , riemann hypothesis , underdetermined system , traffic flow (computer networking) , mathematical optimization , flow (mathematics) , numerical analysis , mathematical analysis , algorithm , geometry , philosophy , computer security , epistemology

We consider a mathematical model for fluid-dynamic flows on networks which is based on conservation laws. Road networks are considered as graphs composed by arcs that meet at some junctions. The crucial point is represented by junctions, where interactions occur and 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 proceeds processing each junction. We present the algorithm and its application to some simple test cases and to portions of urban network.

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