Data-Driven Three-Phase Fundamental Diagram for Traffic Modeling

Abstract

Macroscopic traffic flow models are widely used to estimate traffic status on a freeway, and the fundamental diagram (FD), that establishes a relationship between density and flux, is essential for these models to be effective. By visualizing the 2005 traffic trajectory data from Next Generation SIMulation (NGSIM) project on US Highway 101 and Interstate 80 in California, we observed three states of traffic condition: free flow, mildly congested flow, and highly congested flow; and the resulting shockwaves. The FD is critical in understanding the shockwave phenomenon of congested flow. Therefore, there is a need to develop a more accurate FD that captures the complexity of the density-flux relation observed in the empirical data. For this we develop a three phase FD of traffic flow. In our previous work, a log piecewise linear FD was shown to fit better than some other forms of FD on 2009 traffic data from Interstate 95 in Virginia. However, the previous FD considered two phases, free and congested flow. The three phase modification we propose here is able to distinguish between the highly and the mildly congested flow and explains the resulting shockwaves. The phase transition from mildly to highly congested state changes the nature of the flux-density function from a concave to a convex function of density. In the concave phase a forward moving and in the convex phase a backward moving shock results. This FD can also explain the rarefaction waves that arise in traffic flow. NGSIM data covers every vehicle within its range and we focus our study to the innermost lane. The visualized data is used to fit the three phases. This involved solving an optimization problem to determine the values of the parameters. A close relationship between the backward shockwaves during highly congested phase and the convex part of the FD is observed. A single parameter value (slope of the log-linear function) is shown to predict the various conditions of the traffic: free, mildly and highly congested flow. The proposed FD can be used in conjunction with any macroscopic traffic flow model, such as LighthillWhithamRichards (LWR), for traffic flow estimation with greatly improved accuracy. A three-phase FD and a stochastic macroscopic traffic flow model can reliably predict future traffic status, and provide advanced information to drivers and transportation authorities for travel planning, traffic management, and other real-time applications.