Highlights•First estimate of a 3D-MFD at the urban scale.•3D-MFD model estimates the effects of the vehicle accumulation on speeds.•Discussing the share of public transport users that maximizes the journey speeds.

AbstractTraffic is multi-modal in most cities. However, the impacts of different transport modes on traffic performance and on each other are unclear – especially at the network level. The recent extension of the macroscopic fundamental diagram (MFD) into the 3D-MFD offers a novel framework to address this gap at the urban scale. The 3D-MFD relates the network accumulation of cars and public transport vehicles to the network travel production, for either vehicles or passengers. No empirical 3D-MFD has been reported so far.In this paper, we present the first empirical estimate of a 3D-MFD at the urban scale. To this end, we use data from loop detectors and automatic vehicle location devices (AVL) of the public transport vehicles in the city of Zurich, Switzerland. We compare two different areas within the city, that differ in their topology and share of dedicated lanes for public transport. We propose a statistical model of the 3D-MFD, which estimates the effects of the vehicle accumulation on car and public transport speeds under multi-modal traffic conditions. The results quantify the effects of both, vehicles and passengers, and confirm that a greater share of dedicated lanes reduces the marginal effects of public transport vehicles on car speeds. Lastly, we derive a new application of the 3D-MFD by identifying the share of public transport users that maximizes the journey speeds in an urban network accounting for all motorized transport modes.