Dynamic Model for estimating the Macroscopic Fundamental Diagram

The Macroscopic Fundamental Diagram (MFD) relates the number of circulating vehicles (or accumulation) to a neighbourhood's average speed or flow. In theory the MFD has a well-defined maximum which remains invariant over time. Recent studies, however, suggest that in practice this is not the case, and the MFD does present a variations over time. These variations in the MFD render traffic simulations, modelling and control schemes inaccurate, as these tools do not capture the dynamic nature of the MFD. This paper presents a dynamic model for estimating the MFD, so it does capture the MFD's time varying nature. A mathematical Kalman-filter based framework for solving the model and estimating the MFD are also presented. The application of the method on a small scale example shows the potential of the method.