Introducing a re-sampling methodology for the estimation of empirical macroscopic fundamental diagrams

The uncertainty in the estimation of the macroscopic fundamental diagram (MFD) under real-world traffic conditions and urban dynamics might result in an inaccurate estimation of the MFD parameters—especially if congestion is rarely observed network-wide. For example, as data normally come from punctual observations out of the whole network, it is unclear how representative these observations might be (i.e., how much is the observed capacity affected by the network’s inhomogene-ity). Similarly, if the observed data do not exhibit a distinct congested branch, it is hard to determine the network capacity and critical density. This, in turn, also leads to uncertainties and errors in the parametrization of the MFD for applications, for example traffic control. This paper introduces a novel methodology to estimate (i) the level of inhomogeneity in the network, and (ii) the critical density of the MFD, even when no congested branch is observed. The methodology is based on the idea of re-sampling the empirical data set. Using an extensive data set from Lucerne, Switzerland, and London, UK, insights are provided on the performance and the application of the proposed methodology. The proposed methodology is used to illustrate how the level of inhomogeneity is lower in Lucerne than in the three areas of the network of London that are investigated. The proposed measure of the level of inhomogeneity gives city planners the possibility to analyze and investigate how efficiently their road network is utilized. In addition, the analysis shows that, for the network of Lucerne, the proposed methodology allows accurate estimation of the critical density up to 16 times more often than would be possible otherwise. This simple and robust estimation of the critical density is crucial for the application of many traffic control algorithms.