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

How many cars in the city are too many?: Towards finding the optimal modal split for a multi-modal urban road network

Interactions among different modes or vehicle classes in urban road networks affect the network performance in different and complex ways. Thus, an answer to the question of “how many cars are too many for a city?” is not trivial. However, multi-modal macroscopic fundamental diagrams (MFD) offer a novel opportunity to answer this question. So far, no methodology exists to estimate multi-modal MFDs resulting from arbitrary multi-modal interactions. In this paper, we propose a methodology to capture additional delays in the shape of the MFD and derive an approach for estimating multi-modal MFDs thereof. The influence on the MFD shape is established using the two-fluid theory of urban traffic by defining pairwise copula functions between travel times of each mode. In contrast to many existing approaches, the presented approach retains individual mode’s speed information. We show the approach’s applicability with a tri-modal case of bicycles, buses and cars with empirical data from Amsterdam (NL) and London (UK). Although the approach is not limited to this specific tri-modal case, we use the example to discuss the initial policy question by deriving optimal modal splits for a given accumulation of travelers. Last, we compare the new approach to existing estimation methods for bi-modal MFDs describing car and bus traffic