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Clockwise hysteresis loops in the Macroscopic Fundamental Diagram: An effect of network instability

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  • Gayah, Vikash V.
  • Daganzo, Carlos F.

Abstract

A recent study reported that the Macroscopic Fundamental Diagram of a medium size city exhibited a clockwise hysteresis loop on a day in which a major disturbance caused many drivers to use unfamiliar routes. It is shown below that, even in a perfectly symmetric network with uniform demand, clockwise loops are to be expected when there are disturbances, especially if the disturbances cause a significant fraction of the drivers to not change routes adaptively. It is also shown that when drivers are not adaptive networks are inherently more unstable as they recover from congestion than as they are loaded. In other words, during recovery congestion tends more strongly toward unevenness because very congested areas clear more slowly than less congested areas. Since it is known that uneven congestion distributions reduce network flows, it follows that lower network flows should arise during recovery, resulting in clockwise loops. Fortunately, the presence of a sufficient number of drivers that choose routes adaptively to avoid congested areas helps to even out congestion during recovery, increasing flow. Thus, clockwise loops are less likely to occur when driver adaptivity is high.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:transb:v:45:y:2011:i:4:p:643-655
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Jin, Wen-Long, 2012. "The traffic statics problem in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1360-1373.
    2. Du, Jie & Wong, S.C. & Shu, Chi-Wang & Zhang, Mengping, 2015. "Reformulating the Hoogendoorn–Bovy predictive dynamic user-optimal model in continuum space with anisotropic condition," Transportation Research Part B: Methodological, Elsevier, vol. 79(C), pages 189-217.
    3. 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.
    4. repec:eee:transb:v:106:y:2017:i:c:p:29-51 is not listed on IDEAS
    5. 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.
    6. repec:eee:transe:v:103:y:2017:i:c:p:261-285 is not listed on IDEAS
    7. 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.
    8. Gayah, Vikash V. & Gao, Xueyu (Shirley) & Nagle, Andrew S., 2014. "On the impacts of locally adaptive signal control on urban network stability and the Macroscopic Fundamental Diagram," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 255-268.
    9. Zhang, Lele & Garoni, Timothy M & de Gier, Jan, 2013. "A comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 1-23.
    10. Jin, Wen-Long & Gan, Qi-Jian & Gayah, Vikash V., 2013. "A kinematic wave approach to traffic statics and dynamics in a double-ring network," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 114-131.
    11. Qu, Xiaobo & Wang, Shuaian & Zhang, Jin, 2015. "On the fundamental diagram for freeway traffic: A novel calibration approach for single-regime models," Transportation Research Part B: Methodological, Elsevier, vol. 73(C), pages 91-102.
    12. Saeedmanesh, Mohammadreza & Geroliminis, Nikolas, 2016. "Clustering of heterogeneous networks with directional flows based on “Snake” similarities," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 250-269.
    13. 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.
    14. Du, Jie & Wong, S.C. & Shu, Chi-Wang & Xiong, Tao & Zhang, Mengping & Choi, Keechoo, 2013. "Revisiting Jiang’s dynamic continuum model for urban cities," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 96-119.
    15. 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.
    16. repec:eee:transb:v:111:y:2018:i:c:p:327-355 is not listed on IDEAS
    17. Zhang, Zhao & Parr, Scott A. & Jiang, Hai & Wolshon, Brian, 2015. "Optimization model for regional evacuation transportation system using macroscopic productivity function," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 616-630.
    18. repec:eee:transb:v:104:y:2017:i:c:p:215-237 is not listed on IDEAS
    19. Knoop, Victor L. & van Lint, Hans & Hoogendoorn, Serge P., 2015. "Traffic dynamics: Its impact on the Macroscopic Fundamental Diagram," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 236-250.
    20. repec:eee:transb:v:101:y:2017:i:c:p:245-267 is not listed on IDEAS
    21. repec:eee:transb:v:105:y:2017:i:c:p:193-211 is not listed on IDEAS
    22. 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.
    23. 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.
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    25. repec:eee:transb:v:105:y:2017:i:c:p:523-538 is not listed on IDEAS

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