2020/11/21 by L Vacek, Vacek, Lukáš, Václav Kučera +1
Engineering · Social Sciences · #FOS: Mathematics #Numerical Analysis (math.NA) #Traffic Prediction and Management Techniques #Traffic control and management #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.2011.10862
openalex publication_date 2020/11/21 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this paper, we describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads. On individual roads, we consider the standard Lighthill-Whitham-Richards model which is discretized using the discontinuous Galerkin method along with suitable limiters. In order to solve traffic flows on networks, we construct suitable numerical fluxes at junctions based on preferences of the drivers. We prove basic properties of the constructed numerical flux and the resulting scheme and present numerical experiments, including a junction with complicated traffic light patterns with multiple phases. Differences with the approach to numerical fluxes at junctions from Čanić et al., 2015, are discussed and demonstrated numerically on a simple network.