Data-Fitted First-Order Traffic Models and Their Second-Order Generalizations

Abstract

The Aw–Rascle–Zhang (ARZ) model can be interpreted as a generalization of the first-order Lighthill–Whitham–Richards (LWR) model, with a family of fundamental diagram (FD) curves rather than one. This study investigated the extent to which this generalization increased the predictive accuracy of the models. To that end, two types of data-fitted LWR models and their second-order ARZ counterparts were systematically compared with a version of the test for the three-detector problem. The parameter functions of the models were constructed with historic FD data. The models were then compared with the use of time-dependent data of two types: vehicle trajectory data and single-loop sensor data. These partial differential equation models were studied in a macroscopic sense (i.e., continuous field quantities were constructed from the discrete data, and discretization effects were kept negligibly small).