Open AccessSystems of conservation laws with discontinuous fluxes and applications to traffic
Author(s) -
Massimiliano D. Rosini
Publication year - 2020
Publication title -
annales universitatis mariae curie-skłodowska. sectio a, mathematica
Language(s) - English
Resource type - Journals
eISSN - 2083-7402
pISSN - 0365-1029
DOI - 10.17951/a.2019.73.2.135-173
Subject(s) - conservation law , property (philosophy) , riemann problem , computer science , physical law , traffic flow (computer networking) , riemann hypothesis , microscopic traffic flow model , flow (mathematics) , interface (matter) , mathematical optimization , statistical physics , mathematics , physics , computer security , mathematical analysis , traffic generation model , real time computing , geometry , philosophy , epistemology , bubble , quantum mechanics , maximum bubble pressure method , parallel computing
In this paper we study \(2\times 2\) systems of conservation laws with discontinuous fluxes arising in vehicular traffic modeling. The main goal is to introduce an appropriate notion of solution. To this aim we consider physically reasonable microscopic follow-the-leader models. Macroscopic Riemann solvers are then obtained as many particle limits. This approach leads us to develop six models. We propose a unified way to describe such models, which highlights their common property of maximizing the density flow across the interface under appropriate physical restrictions depending on the case at hand.