Identification and characterizing of the prevailing paths on a urban network for MFD-based applications

One of the main challenges for multi-regional application of the aggregated traffic models based on the Macroscopic Fundamental Diagram, lies in the identification and characterization of the most prevailing paths chosen by drivers. In this paper, we propose a methodological framework, based on two distinct methods, to determine these prevailing paths. The first method requires the information about travel patterns in the urban network as well as the information about the city network partitioning. The second method is more parsimonious, and consists on the direct calculation of shortest-cost paths on the aggregated network. For this, we propose four impedance functions that utilize topological features of the urban network and its partitioning. We test the performance of this methodological framework for determining the most prevailing paths on a network representing the metropolitan area of Lyon (France). We consider a set of real trajectories (i.e. GPS data) of drivers in this network as a benchmark. We show that the proposed methods are able to identify the most prevailing paths as the ones chosen by drivers, as evidenced by a large similarity value between the sets of paths. Based on a maximum likelihood estimation, we also show that the Weibull distribution is the one that better reproduces the functional form of the network-wide distribution of travel distances. However, the characterization of the functional form of such distributions characteristic to each region defining a path is not trivial, and depends on the complex topological features of the urban network concerning the definition of its partitioning. We also show that the Euclidean distance metrics provides good estimates of the average travel distances. Interestingly, we also show that the most prevailing paths are not necessarily the ones that have the lowest average travel distances.