Empirics of a Generalized Macroscopic Fundamental Diagram for Urban Freeways

Because of an increasing exchange of data between measurement sites, the area over which traffic control is applied is also increasing. This situation leads to three new challenges: (a) working with the large quantities of data (transmit, store), (b) estimating the traffic state, and (c) controlling a large area with many controllers (and thus large solution space). This paper introduces a new way of describing the traffic state for a large area, one that requires much less data and nevertheless gives an accurate representation of the state. The macroscopic fundamental diagram (MFD) links the production (the average flow) to the accumulation (the average number of vehicles) in an area. This paper shows that MFD can be converted to a generalized MFD (GMFD) for urban freeways; the GMFD relates the production to the accumulation and the spatial spread of density. Analysis of 10 months of data from the Amsterdam, Netherlands, ring road freeway showed that GMFD is a continuous function that increases and decreases with accumulation, as does a fundamental diagram, and decreases with the spatial spread of density. The predictive performance of GMFD was tested with a nonparameterized fit and by fitting a functional form; each test performed equally well. Predicting the production is important, especially near the maximum production. GMFD explains much more of the spread in the production than MFD does, especially near this maximum production. Thus, this lean traffic state description can be used in setting a target for traffic control.