A non-local traffic flow model for 1-to-1 junctions with buffer

Networks and Heterogeneous Media, vol. 19, pp. 405–429

Abstract

In this paper, we introduce a non-local PDE-ODE traffic model devoted to the description of a 1-to-1 junction with buffer. We present an existence result in the free flow case as well as a numerical method to approximate weak solutions in the general case. In addition, we show a maximum principle, which is uniform in the non-local interaction range. Further, we exploit the limit models as the support of the kernel tends to zero and to infinity. We compare them with other already existing models for traffic and production flow and presented numerical examples.

Authors 3

1. Felisia Angela Chiarello

   University of L'Aquila

   Affiliation as printed

   DISIM, University of L'Aquila, Via Vetoio Ed. Coppito 1, 67100 L'Aquila, Italy

2. Jan O. Friedrich Aachen

   RWTH Aachen University

   Affiliation as printed

   IGPM, RWTH Aachen University, Templergraben 55, 52064 Aachen, Germany

3. Simone Göttlich corresponding Aachen

   RWTH Aachen University · University of Mannheim · University of L'Aquila

   Affiliation as printed

   Department of Mathematics, University of Mannheim, B6, 28-29, 68159 Mannheim, Germany

   DISIM, University of L'Aquila, Via Vetoio Ed. Coppito 1, 67100 L'Aquila, Italy

   IGPM, RWTH Aachen University, Templergraben 55, 52064 Aachen, Germany