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Estimating MFDs in simple networks with route choice

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  • Leclercq, Ludovic
  • Geroliminis, Nikolas

Abstract

The concept of the Macroscopic Fundamental Diagram (MFD) is elegant and attractive because it provides a global view of traffic behavior and performance at a network level. However, recent research shows that the MFD shape can be influenced by local traffic heterogeneities. Notably, route choices and heterogeneous local capacities may drive uneven (in space) or inconsistent (in time) distributions of congestion and then affect the shape and the scatter of the MFD. We are far from having a global understanding of the connections between local phenomena and the resulting MFD. This paper first aims to improve existing MFD estimation method for a succession of links with traffic signals. The new method overcomes previous limitations, notably regarding to the topology and signal settings regularities, by fully utilizing the receipts of the variational theory. Then, a single network with several parallel routes is investigated. MFDs on different routes are estimated with the variational method and then aggregated in a unified MFD for stationary and dynamic conditions and different sorts of equilibria (user and system optimum). It appears that the flow distribution among routes smoothly varies with respect to the total flow either in free-flow or congestion situations. Such a distribution is much more rough for system optimum, where it presents some discontinuities and is far from equity. This means that a control strategy able to lead such a network to the perfect system optimum would be hard to tune, especially in the congested regime. However, being able to determine the MFD corresponding to the system optimum provides a valuable reference to estimate the current efficiency of the considered network. Case studies for different simple networks and insights for generalization at the city level are proposed.

Suggested Citation

  • Leclercq, Ludovic & Geroliminis, Nikolas, 2013. "Estimating MFDs in simple networks with route choice," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 468-484.
    • Handle: RePEc:eee:transb:v:57:y:2013:i:c:p:468-484
    DOI: 10.1016/j.trb.2013.05.005
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    References listed on IDEAS

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    1. Cassidy, Michael J., 1998. "Bivariate relations in nearly stationary highway traffic," Transportation Research Part B: Methodological, Elsevier, vol. 32(1), pages 49-59, January.
    2. Haddad, Jack & Ramezani, Mohsen & Geroliminis, Nikolas, 2013. "Cooperative traffic control of a mixed network with two urban regions and a freeway," Transportation Research Part B: Methodological, Elsevier, vol. 54(C), pages 17-36.
    3. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: basic theory and complex boundary conditions," Transportation Research Part B: Methodological, Elsevier, vol. 39(2), pages 187-196, February.
    4. Geroliminis, Nikolas & Sun, Jie, 2011. "Properties of a well-defined macroscopic fundamental diagram for urban traffic," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 605-617, March.
    5. Geroliminis, Nikolas & Daganzo, Carlos F., 2008. "Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 759-770, November.
    6. Daganzo, Carlos F. & Gayah, Vikash V. & Gonzales, Eric J., 2011. "Macroscopic relations of urban traffic variables: Bifurcations, multivaluedness and instability," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 278-288, January.
    7. Ji, Yuxuan & Geroliminis, Nikolas, 2012. "On the spatial partitioning of urban transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1639-1656.
    8. Daganzo, Carlos F., 2005. "A variational formulation of kinematic waves: Solution methods," Transportation Research Part B: Methodological, Elsevier, vol. 39(10), pages 934-950, December.
    9. Geroliminis, Nikolas & Boyacı, Burak, 2012. "The effect of variability of urban systems characteristics in the network capacity," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1607-1623.
    10. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    11. Daganzo, Carlos F. & Geroliminis, Nikolas, 2008. "An analytical approximation for the macroscopic fundamental diagram of urban traffic," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 771-781, November.
    12. Daganzo, Carlos F & Geroliminis, Nikolas, 2008. "An analytical approximation for the macropscopic fundamental diagram of urban traffic," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt4cb8h3jm, Institute of Transportation Studies, UC Berkeley.
    13. Amin Mazloumian & Nikolas Geroliminis & Dirk Helbing, "undated". "The Spatial Variability of Vehicle Densities as Determinant of Urban Network Capacity," Working Papers CCSS-09-009, ETH Zurich, Chair of Systems Design.
    14. Keyvan-Ekbatani, Mehdi & Kouvelas, Anastasios & Papamichail, Ioannis & Papageorgiou, Markos, 2012. "Exploiting the fundamental diagram of urban networks for feedback-based gating," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1393-1403.
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