Communications in Mathematical Sciences

Volume 16 (2018)

Number 1

Priority-based Riemann solver for traffic flow on networks

Pages: 185 – 211



Maria Laura Delle Monache (Department of Mathematical Sciences, Rutgers University, Camden, New Jersey, U.S.A.; and Inria, Université Grenoble Alpes, Grenoble, France)

Paola Goatin (Inria, Sophia Antipolis Méditerranée, Université Côte d’Azur, Sophia Antipolis, France)

Benedetto Piccoli (Department of Mathematical Sciences and CCIB, Rutgers University, Camden, New Jersey, U.S.A)


In this article we introduce a new Riemann solver for traffic flow on networks. The Priority Riemann solver ($\mathcal{PRS}$) 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.


scalar conservation laws, traffic flow, Riemann solver

2010 Mathematics Subject Classification

35L65, 90B20

This research was supported by the NSF grant CNS #1446715, by KI-Net “Kinetic description of emerging challenges in multiscale problems of natural sciences” - NSF grant # 1107444 and by the INRIA associated team Optimal REroute Strategies for Traffic managEment (ORESTE).

Published 29 March 2018