Abstract
We extend the Phase Transition model for traffic proposed in [8], by Colombo, Marcellini, and Rascle to the network case. More precisely, we consider the Riemann problem for such a system at a general junction with $n$ incoming and $m$ outgoing roads. We propose a Riemann solver at the junction which conserves both the number of cars and the maximal speed of each vehicle, which is a key feature of the Phase Transition model. For special junctions, we prove that the Riemann solver is well defined.
Highlights
This paper deals with Riemann problems at junctions for a macroscopic phase transition traffic model
The fundamental diagram is composed by the Free phase F and the Congested phase C
In the free phase the model is the classical LWR one, while in the congested phase it consists on a system of two differential equations
Summary
This paper deals with Riemann problems at junctions for a macroscopic phase transition traffic model. We consider a Riemann problem at a junction and we propose a Riemann solver, which conserves both the number of cars and the maximal speed w of each driver, a key feature of (1), which can be interpreted as a Lagrangian marker; see [8, 14, 19]. This is in the same spirit as the Riemann solver, proposed by Herty and Rascle in [14] and by Herty, Moutari and Rascle in [13] for the ARZ model. On each arc we consider the phase transition model in (1)
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