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
Garavello, M., Marcellini, F. (2017). The Riemann problem at a junction for a Phase Transition traffic model. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 37(10), 5191-5209 [10.3934/dcds.2017225].
The Riemann problem at a junction for a Phase Transition traffic model
Garavello, M
;Marcellini, F.
2017
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
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