Higher-Order Traffic Flow Model Extended to Road Networks

In this work, a conserved higher-order (CHO) macroscopic traffic flow model is extended to road networks. We first introduce the Riemann problem at a junction for the CHO model and then provide a general framework to solve it, considering the compatibility between the CHO and Lighthill-Whitham-Richards (LWR) models. Through the presented framework, Riemann solvers for the LWR model can be extended to the CHO model. Specifically, a kind of Riemann solver for the LWR model is extended to derive the Riemann solver for the CHO model, in which the total actual flow at the junction is maximized. The Riemann solvers for three typical junctions (one-in-two-out junction, two-in-one-out junction, and two-in-two-out junction) are discussed. The first-order finite-volume method is adopted to solve the extended model. Numerical examples are given to validate the extended model and the numerical algorithm.