We consider a junction regulated by a traffic lights, with n incoming roads and only one outgoing road. On each road the Phase Transition traffic model, proposed in [6], describes the evolution of car traffic. Such model is an extension of the classic Lighthill–Whitham–Richards one, obtained by assuming that different drivers may have different maximal speed. By sending to infinity the number of cycles of the traffic lights, we obtain a justification of the Riemann solver introduced in [9] and in particular of the rule for determining the maximal speed in the outgoing road.

Garavello, M., Marcellini, F. (2018). A Riemann solver at a junction compatible with a homogenization limit. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 464(2), 1333-1351 [10.1016/j.jmaa.2018.04.068].

A Riemann solver at a junction compatible with a homogenization limit

Abstract

We consider a junction regulated by a traffic lights, with n incoming roads and only one outgoing road. On each road the Phase Transition traffic model, proposed in [6], describes the evolution of car traffic. Such model is an extension of the classic Lighthill–Whitham–Richards one, obtained by assuming that different drivers may have different maximal speed. By sending to infinity the number of cycles of the traffic lights, we obtain a justification of the Riemann solver introduced in [9] and in particular of the rule for determining the maximal speed in the outgoing road.
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Articolo in rivista - Articolo scientifico
Continuum traffic models; Homogenization limit; Hyperbolic systems of conservation laws; Phase transition model;
Continuum traffic models; Homogenization limit; Hyperbolic systems of conservation laws; Phase transition model; Analysis; Applied Mathematics
English
2018
464
2
1333
1351
none
Garavello, M., Marcellini, F. (2018). A Riemann solver at a junction compatible with a homogenization limit. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 464(2), 1333-1351 [10.1016/j.jmaa.2018.04.068].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/199664`
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