Modeling and characteristics of the fundamental diagram for lagrangian-space kinematic wave model

With the emergence of probe vehicle technologies, the Lagrangian LWR (Lighthill-Whitham-Richards) model has received increasing interests due to its numerical accuracy and efficiency, as well as the ease of formulating mobile sensor data. The objective of this paper is to investigate the empirical p-? model for the Lagrangian-space model recently introduced in Hamilton-Jacobi theory. In this paper, we proposed a piecewise formulation for the p-? model and conducted a regression analysis based on the field traffic flow data. The regression results demonstrated the concentration of the p-? diagram: R square is 0.75 for the p-? diagram but 0.58 for the q-k diagram which is often used for the Euler coordinate based on the same field data. Meanwhile, the p-? model was found to be continuous. Thus, the partial differential equations can be formulated and conducted simply eliminating discontinuous points. Finally, the hysteresis loop characteristic was also investigated, and most loops were found to be clockwise. Therefore, for the p-? model, the potential benefit in traffic condition (especially jam) recognition, as well as the outstanding accuracy in the regression analysis will be achieved. What's more, the methodology and models in this article can provide valuable insights for the capacity calculation and the MFD (Macroscopic Fundamental Diagram) modeling in traffic engineering.