A general framework for multi-modal macroscopic fundamental diagrams (MFD)

Car traffic streams in urban networks are rarely homogeneous and usually contain some disturbances by other transport modes of different physical characteristics, e.g. bicycles or buses. Inevitably, these interactions decrease the network’s capacity and performance, but, so far, no methodology exists to assess the local interaction effects on the network level as for instance described in the macroscopic fundamental diagram (MFD). This paper proposes an analytical framework to link general microscopic disturbances to the shape of the MFD and thus to network capacity. The influence of disturbances is established by linking the two-fluid theory of urban traffic to travel times derived from the MFD. We apply the framework to the interactions of bicycles, buses and cars with an empirical calibration using data from London (UK). This framework allows to identify the maximum possible travel production of a given network and its associated modal split, as well as to identify for a given demand the optimal modal split