Priority-based Riemann solver for traffic flow on networks

Maria Laura Delle Monache (1, 2) , Paola Goatin (3) , Benedetto Piccoli (1)

1 Department of Mathematical Sciences [Camden]
2 NECS - Networked Controlled Systems
3 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences

In this article we introduce a new Riemann solver for traffic flow on networks. The Priority Riemann solver (PRS) provides a solution at junctions by taking into consideration priorities for the incoming roads and maximization of through flux. We prove existence of solutions for the solver for junctions with up to two incoming and two outgoing roads and show numerically the comparison with previous Riemann solvers. Additionally, we introduce a second version of the solver that considers the priorities as softer constraints and illustrate numerically the differences between the two solvers.

Mots clés: Scalar conservation laws; Traffic flow; Riemann solver

Domaines: Equations aux dérivées partielles [math.AP]

Maria Laura Delle Monache, Paola Goatin, Benedetto Piccoli. Priority-based Riemann solver for traffic flow on networks. Communications in Mathematical Sciences, 2018, 16 (1), pp.185-211. ⟨10.4310/CMS.2018.v16.n1.a9⟩. ⟨hal-01336823⟩