A Riemann solver at a junction compatible with a homogenization limit

2017/12/20 by Garavello, Mauro, Marcellini, Francesca
#35L65 #90B20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.07677

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.

Related

• The Riemann Solver for Traffic Flow at an Intersection with Buffer of\n Vanishing Size
• A class of germs arising from homogenization in traffic flow on junctions
• Pareto-optimal coupling conditions for the Aw-Rascle-Zhang traffic flow model at junctions
• A macroscopic traffic flow model with phase transitions and local point constraints on the flow
• A Riemann solver for a system of hyperbolic conservation laws at a general road junction