Lukas Ambühl

Introducing a re-sampling methodology for the estimation of empirical macroscopic fundamental diagrams

The uncertainty in the estimation of the macroscopic fundamental diagram (MFD) under real-world traffic conditions and urban dynamics might result in an inaccurate estimation of the MFD parameters—especially if congestion is rarely observed network-wide. For example, as data normally come from punctual observations out of the whole network, it is unclear how representative these observations might be (i.e., how much is the observed capacity affected by the network’s inhomogeneity). Similarly, if the observed data do not exhibit a distinct congested branch, it is hard to determine the network capacity and critical density. This, in turn, also leads to uncertainties and errors in the parametrization of the MFD for applications, for example traffic control. This paper introduces a novel methodology to estimate (i) the level of inhomogeneity in the network, and (ii) the critical density of the MFD, even when no congested branch is observed. The methodology is based on the idea of re-sampling the empirical data set. Using an extensive data set from Lucerne, Switzerland, and London, UK, insights are provided on the performance and the application of the proposed methodology. The proposed methodology is used to illustrate how the level of inhomogeneity is lower in Lucerne than in the three areas of the network of London that are investigated. The proposed measure of the level of inhomogeneity gives city planners the possibility to analyze and investigate how efficiently their road network is utilized. In addition, the analysis shows that, for the network of Lucerne, the proposed methodology allows accurate estimation of the critical density up to 16 times more often than would be possible otherwise. This simple and robust estimation of the critical density is crucial for the application of many traffic control algorithms.

The MFD and the built environment – A new perspective on traffic problems in towns

1 Travel behavior in urban areas has been widely analyzed from the demand side, while the extent 2 to which the infrastructure imposes constraints on such travel behavior and leads to delays and 3 congestion has almost never been studied. For car-based transportation, the recently developed 4 theory of the macroscopic fundamental diagram (MFD) describes the relationship between the 5 accumulation of vehicles and their trip ending rate as a function of the infrastructure, opening the 6 door to new and meaningful studies that address the gap mentioned above. In this paper, we use 7 empirical traffic data from 42 cities around the world to estimate their MFDs, compare them with 8 respect to their functional behavior and the extent of delays, and explain the observed differences 9 as a function of the network topology, e.g. intersection density, average betweeness. We find 10 that the average betweenness centrality in a network seems to be a very clear indicator for the 11 level of traffic performance. This indicates that it is indeed possible to use some topological 12 features to predict traffic performance at the macroscopic level. 13 Loder, A., L. Ambühl, M. Menendez and K. W. Axhausen 2

Empirics of multimodal traffic networks - Using the 3D macroscopic fundamental diagram

Traffic is multimodal 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) to the 3D-MFD, offers a novel framework to address this gap at the urban scale. The 3D-MFD relates the network density of cars and public transport vehicles to the network flow, 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 to public transport. We propose a statistical model of the 3D-MFD, which estimates the effects of the demands on car and public transport speeds. The results quantify the multimodal effects of both, vehicles and passengers, and confirms that a greater share of dedicated lanes reduces the marginal effect 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.