Second-Order Traffic Flow Models on Networks

Abstract

This paper deals with the Aw-Rascle-Zhang [2,31] model for traffic flow on unidirectional road networks. We construct weak solutions to Riemann problems at the junctions, which conserve the mass and the generalized momentum. In particular, we introduce a new approach to approximate the homogenized pressure through an additional equation for the propagation of a reference pressure. The resulting system of coupled conservation laws is then solved using an appropriate numerical scheme of Godunov type. Numerical simulations show that the proposed approach enables to approximate the homogenized pressure sufficiently well. The features of the new approach are illustrated through a comparative analysis with other methods proposed in the literature, namely [13,19,16,23,28], for the second order traffic model [2,31] and the Lighthill-Whitham-Richards model [26,27].

Data‐driven models for traffic flow at junctions

“…We note that the density flow obtained from the Greenshield model () attains maximal flow at density $$$ {\sigma}^k={\rho}_{\mathrm{max}}^k/2 $$$. Demand and supply have also been defined for ARZ‐type models in the literature [30, 33, 37].…”

“…Existence and uniqueness of network solution for suitable coupling rules has been established in the literature [9, 25]. These results have also been extended to second‐order models in the literature [30, 37].…”

“…In Göttlich et al [37], another coupling approach has been considered. If the coupling of model C3 is applied to the ARZ model, then, the priority will influence also the pressure $$$ p\left(\rho, w\right) $$$ on the outgoing road.…”

“…Coupling conditions for ARZ models have been proposed, for example, in the literature [9,21,[26][27][28][29][30][31][32][33][34], whereas in previous studies [35,36], the authors proposed coupling conditions for ARZ phase transition models. We also refer to Göttlich et al [37] for a comparison and novel conditions. Typically, well-posedness results are obtained using the notion of (nodal or half-) Riemann solvers to classify consistent boundary conditions.…”

“…In particular, a new class of machine learning models is proposed that combine trained artificial neural networks with a parametrization of the solution space of the half-Riemann problem at the junction to substitute for the nonlinear coupling conditions. We compare numerically the predictions of the novel models with existing classical models taken from previous works [9,37]. We not only compare the coupling conditions but also conduct long-time predictions for upstream and downstream traffic simulated through a finite-volume method.…”