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Macroscopic urban dynamics: Analytical and numerical comparisons of existing models

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  • Mariotte, Guilhem
  • Leclercq, Ludovic
  • Laval, Jorge A.

Abstract

Large-scale network modeling using the Macroscopic Fundamental Diagram (MFD) is widely based on the single-reservoir model, where the variation of the accumulation of circulating vehicles in the reservoir equals inflow minus outflow. However, inconsistent lags for information propagation between boundaries may be observed with this single accumulation-based model. For example, outflow is reacting too fast when inflow varies rapidly, whereas this information should be carried by vehicles that are never driving faster than the free-flow speed. To overcome this limitation, a trip-based model has been recently proposed, but whose solution cannot be obtained analytically.

Suggested Citation

  • Mariotte, Guilhem & Leclercq, Ludovic & Laval, Jorge A., 2017. "Macroscopic urban dynamics: Analytical and numerical comparisons of existing models," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 245-267.
    • Handle: RePEc:eee:transb:v:101:y:2017:i:c:p:245-267
    DOI: 10.1016/j.trb.2017.04.002
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    References listed on IDEAS

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    1. Daganzo, Carlos F., 2011. "On the macroscopic stability of freeway traffic," Transportation Research Part B: Methodological, Elsevier, vol. 45(5), pages 782-788, June.
    2. Laval, Jorge A. & Castrillón, Felipe, 2015. "Stochastic approximations for the macroscopic fundamental diagram of urban networks," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 904-916.
    3. Ramezani, Mohsen & Haddad, Jack & Geroliminis, Nikolas, 2015. "Dynamics of heterogeneity in urban networks: aggregated traffic modeling and hierarchical control," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 1-19.
    4. Laval, Jorge A. & Chilukuri, Bhargava R., 2016. "Symmetries in the kinematic wave model and a parameter-free representation of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 168-177.
    5. Haddad, Jack, 2017. "Optimal perimeter control synthesis for two urban regions with aggregate boundary queue dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 96(C), pages 1-25.
    6. Fosgerau, Mogens, 2015. "Congestion in the bathtub," Economics of Transportation, Elsevier, vol. 4(4), pages 241-255.
    7. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part II: Queueing at freeway bottlenecks," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 289-303, August.
    8. Newell, G. F., 1993. "A simplified theory of kinematic waves in highway traffic, part I: General theory," Transportation Research Part B: Methodological, Elsevier, vol. 27(4), pages 281-287, August.
    9. Kouvelas, Anastasios & Saeedmanesh, Mohammadreza & Geroliminis, Nikolas, 2017. "Enhancing model-based feedback perimeter control with data-driven online adaptive optimization," Transportation Research Part B: Methodological, Elsevier, vol. 96(C), pages 26-45.
    10. Geroliminis, Nikolas, 2015. "Cruising-for-parking in congested cities with an MFD representation," Economics of Transportation, Elsevier, vol. 4(3), pages 156-165.
    11. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.
    12. Gayah, Vikash V. & Daganzo, Carlos F., 2011. "Clockwise hysteresis loops in the Macroscopic Fundamental Diagram: An effect of network instability," Transportation Research Part B: Methodological, Elsevier, vol. 45(4), pages 643-655, May.
    13. Yildirimoglu, Mehmet & Geroliminis, Nikolas, 2014. "Approximating dynamic equilibrium conditions with macroscopic fundamental diagrams," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 186-200.
    14. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    15. Daganzo, Carlos F. & Lehe, Lewis J., 2015. "Distance-dependent congestion pricing for downtown zones," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 89-99.
    16. Haddad, Jack & Geroliminis, Nikolas, 2012. "On the stability of traffic perimeter control in two-region urban cities," Transportation Research Part B: Methodological, Elsevier, vol. 46(9), pages 1159-1176.
    17. Geroliminis, Nikolas & Sun, Jie, 2011. "Hysteresis phenomena of a Macroscopic Fundamental Diagram in freeway networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(9), pages 966-979, November.
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