Analytical method to approximate the impact of turning on the macroscopic fundamental diagram

Network macroscopic fundamental diagrams (MFDs) have recently been shown to exist in real-world urban traffic networks. The existence of an MFD facilitates the modeling of urban traffic network dynamics at a regional level, which can be used to identify and refine large-scale network-wide control strategies. To be useful, MFD-based modeling frameworks require an estimate of the functional form of a network’s MFD. Analytical methods have been proposed to estimate a network’s MFD by abstracting the network as a single ring-road or corridor and modeling the flow–density relationship on that simplified element. However, these existing methods cannot account for the impact of turning traffic, as only a single corridor is considered. This paper proposes a method to estimate a network’s MFD when vehicles are allowed to turn into or out of a corridor. A two-ring abstraction is first used to analyze how turning will affect vehicle travel in a more general network, and then the model is further approximated using a single ring-road or corridor. This approximation is useful as it facilitates the application of existing variational theory-based methods (the stochastic method of cuts) to estimate the flow–density relationship on the corridor, while accounting for the stochastic nature of turning. Results of the approximation compared with a more realistic simulation that includes features that cannot be captured using variational theory—such as internal origins and destinations—suggest that this approximation works to estimate a network’s MFD when turning traffic is present.



Work Title Analytical method to approximate the impact of turning on the macroscopic fundamental diagram
Open Access
  1. Guanhao Xu
  2. Zhengyao Yu
  3. Vikash V. Gayah
License In Copyright (Rights Reserved)
Work Type Article
  1. Transportation Research Record
Publication Date July 3, 2020
Publisher Identifier (DOI)
Deposited November 18, 2021




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Version 1

  • Created
  • Added MFD_with_turning_2020.05.19.docx
  • Added Creator Guanhao Xu
  • Added Creator Zhengyao Yu
  • Added Creator Vikash V. Gayah
  • Published
  • Updated
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