From Corridor to Network Macroscopic Fundamental Diagrams: A Semi-Analytical Approximation Approach

Gabriel Tilg (), Lukas Ambühl (), Sérgio F. A. Batista (), Mónica Menéndez (), Ludovic Leclercq () and Fritz Busch ()
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Gabriel Tilg: Chair of Traffic Engineering and Control, Department of Civil, Geo, and Environmental Engineering, Technical University of Munich, 80333 Munich, Germany
Lukas Ambühl: Traffic Engineering Group, Institute for Transport Planning and Systems, ETH Zurich, 8093 Zurich, Switzerland
Sérgio F. A. Batista: Division of Engineering, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates
Mónica Menéndez: Division of Engineering, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates
Ludovic Leclercq: Université Gustave Eiffel, ENTPE, LICIT, F-69518 Lyon, France
Fritz Busch: Chair of Traffic Engineering and Control, Department of Civil, Geo, and Environmental Engineering, Technical University of Munich, 80333 Munich, Germany

Transportation Science, 2023, vol. 57, issue 5, 1115-1133

Abstract: The design of network-wide traffic management schemes or transport policies for urban areas requires computationally efficient traffic models. The macroscopic fundamental diagram (MFD) is a promising tool for such applications. Unfortunately, empirical MFDs are not always available, and semi-analytical estimation methods require a reduction of the network to a corridor that introduces substantial inaccuracies. We propose a semi-analytical methodology to estimate the MFD for realistic urban networks without the information loss induced by the reduction of networks to corridors. The methodology is based on the method of cuts but applies to networks with irregular topologies, accounts for different spatial demand patterns, and determines the upper bound of network flow. Therefore, we consider both flow conservation and the effects of spillbacks at the network level. Our framework decomposes a given network into a set of corridors, creates a hypernetwork, including the impacts of source terms, and then treats the dependencies across corridors (e.g., because of turning flows and spillbacks). Based on this hypernetwork, we derive the free-flow and capacity branch of the MFD. The congested branch is estimated by considering gridlock characteristics and utilizing recent advancements in MFD research. We showcase the applicability of the proposed methodology in a case study with a realistic setting based on the Sioux Falls network. We then compare the results to the original method of cuts and a ground truth derived from the cell transmission model. This comparison reveals that our method is more than five times more accurate than the state of the art in estimating the network-wide capacity and jam density. Moreover, the results clearly indicate the MFD’s dependency on spatial demand patterns. Compared with simulation-based MFD estimation approaches, the potential of the proposed framework lies in the modeling flexibility, explanatory value, and reduced computational cost.

Keywords: macroscopic fundamental diagram; method of cuts; network modeling; traffic flow theory; variational theory (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:57:y:2023:i:5:p:1115-1133

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