A Day-to-day Invariant Macroscopic Fundamental Diagrams for Probe Vehicles

The macroscopic fundamental diagram (MFD) for an urban area provides a new thought on aggregate traffic management and control that are less affected by details. The MFD is conventionally constructed by using loop detector data, which may not widely exist due to the limited coverage of hardware installation. In contrast, the probe vehicle data have the benefits of low cost and wide coverage. To make use of the widely existing low cost data, we propose an MFD for probe vehicles (pMFD). Taking Beijing road network as an example, we empirically demonstrate that the pMFD is day-to-day invariant in shape. We then explicitly analyse the relation between the pMFD and the conventional MFD. This study relaxes the data constraint of the MFD construction and provides a new insight on macroscopic network condition monitoring.