On micro-macro derivation of traffic flow models with $(A,B)$-connection and its stability

Abstract

We show that $(A,B)$-connections for conservations laws with a flux discontinuity can be obtained as limits of perturbed Follow-the-Leader (FtL) models, and provide continuity and surjectivity of the map associating the perturbation of the dynamics with the flux limiter.

arXiv comment32 pages