Investigating the Properties and Existence of a Macroscopic Fundamental Diagram for Arterial and Freeway Traffic Systems

University of Minnesota Master of Science thesis. September 2009. Major: Civil Engineering. Advisor: Nikolas Geroliminis. 1 computer file (PDF); viii, 61 pages.A field experiment in Yokohama (Japan) revealed that a macroscopic fundamental diagram (MFD) linking space-mean flow , density and speed exists on a large urban area. Despite these and other recent findings for the existence of well defined MFDs for urban areas, these MFDs should not be universally expected. In this thesis, the properties of a well defined MFD are investigated and it is found out that the spatial distribution of density/occupancy in the network is one of the key components that affect the scatter of an MFD and its shape. An analytical derivation of the spatial distribution that considers correlation between adjacent links has also been proposed. The scatter of an MFD in terms of errors in probability density function of spatial occupancy and errors of individual links' fundamental diagram (FD) have also been investigated and an analytical estimation of the errors is provided. Using real data from detectors for an urban arterial and a freeway network we validate the proposed derivations and we show that an MFD is not well defined in freeway networks as hysteresis effects are present. The hysteresis phenomenon in network is investigated at different levels of the network and it is found out that the heterogeneity of the network and the hysteresis in the individual detectors should account for this phenomenon. The datasets in this paper consist of flow and occupancy measures from 500 fixed sensors in the Yokohama downtown area and 600 loop detectors in the Twin Cities Metropolitan Area Freeway network (Minnesota, USA)