Numerical approximations of a traffic flow model on networks. (English) Zbl 1124.90005

In the 1950s James Lighthill and Gerald Whitham and independently P. I. Richards proposed to apply fluid dynamic concepts to traffic. This leads to a hyperbolic conservation law that models the flow of cars in a single road. In this paper, traffic flow on a network of roads as in the urban context is considered. Junctions play a fundamental role, since the system is underdetermined even after prescribing the conservation of cars that can be written as the Rankine-Hugoniot condition. To determine a unique solution to Riemann problems at junctions, two criteria are assumed: (A) There are some fixed coefficients, the prescribed preferences of drivers, that express the distribution of traffic from incoming to outgoing roads; (B) Respecting (A), drivers’ choices are made in order to maximize the flux. The numerical approximation is carried out by the Godunov scheme and discrete velocities kinetic schemes. The algorithms are presented and some small portions of urban networks are considered as test cases.


90B20 Traffic problems in operations research
34B45 Boundary value problems on graphs and networks for ordinary differential equations
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