A Linearizing Transformation-Based Evaluation Approach of the Fundamental Diagram

The fundamental diagram (FD) describes the functional relationship among macro parameters of traffic flow (e.g., volume, density, and space mean speed). A well-established FD is crucial for traffic operations and management (e.g., traffic estimation and control). However, there is still lacking an efficient method to select a FD and evaluate the fitting performance with empirical data. In this paper, we propose a novel evaluation approach to the FD using a linear transformation method, which can evaluate the fitting performance in the whole density region. It can also provide directions for further optimization of the FD model by performing the same transformation on the empirical dataset and the selected FD. Furthermore, we propose a quantitative indicator, called the weighted coefficient of determination, which can better evaluate the fitting performance of different FDs. The proposed method is tested with freeway field data from loop detectors. The results show that the proposed evaluation method can help select the FD that fits the empirical dataset best. The evaluation results can also be used to analyze the systematic deviation ignored by those FDs that cannot fit the data well to further improve FD models.