On the use of Lagrangian observations from public transport and probe vehicles to estimate car space-mean speeds in bi-modal urban networks

The Macroscopic Fundamental Diagram (MFD) has been recognized as a powerful framework to develop network-wide control strategies. Recently, the concept has been extended to the three-dimensional MFD, used to investigate traffic dynamics of multi-modal urban cities, where different transport modes compete for, and share the limited road infrastructure. In most cases, the macroscopic traffic variables are estimated using either loop detector data (LDD) or floating car data (FCD). Taking into account that none of these data sources might be available, in this study we propose novel estimation methods for the space-mean speed of cars based on: (i) the automatic vehicle location (AVL) data of public transport where no FCD is available; and (ii) the fused FCD and AVL data sources where both are available, but FCD is not complete. Both methods account for the network configuration layout and the configuration of the public transport system. The first method allows one to derive either uni-modal or bi-modal macroscopic fundamental relationships, even in the extreme cases where no LDD nor FCD exist. The second method does not require a priori knowledge about FCD penetration rates and can significantly improve the estimation accuracy of the macroscopic fundamental relationships. Using empirical data from the city of Zurich, we demonstrate the applicability and validate the accuracy of the proposed methods in real-life traffic scenarios, providing a cross-comparison with the existing estimation methods. Such empirical comparison is, to the best of our knowledge, the first of its kind. The findings show that the proposed AVL-based estimation method can provide a good approximation of the average speed of cars at the network level. On the other hand, by fusing the FCD and AVL data, especially in case of sparse FCD, it is possible to obtain a more representative outcome regarding the performance of multi-modal traffic.