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Analytical approximation and calibration of roundabout capacity: A merging state transition-based modeling approach

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  • Song, Yang
  • Hu, Xianbiao
  • Lu, Jiawei
  • Zhou, Xuesong

Abstract

This manuscript focuses on the theoretical advancement of causality between entry vehicle dynamics and roundabout capacity modeling, with a merging state transition-based analytical approximation and calibration approach. Gap acceptance models, such as the HCM model, usually ignore roundabout specific operating conditions, whereas empirical models are generally criticized for the lack of fundamental understanding of underlying traffic flow or driving behaviors. The roundabout geometry is firstly extracted into a Y-shaped network, and the traffic movements are illustrated with a state-space-time diagram. Next, we analyze the merging state space for the entry vehicles, and draw the state-transition diagram. The episode of a traffic flow is defined, and we show that the trajectory of an entry vehicle repeats one of four patterns within each episode. Then, state transition-based analytical derivation of roundabout capacity is presented. This is done by estimating the state transition probabilities, followed by an episode-based state transition chain analysis and, finally, finding the solution of state transitions under steady states. Circulating speed is used as a key variable to reflect the operating conditions in the target roundabout. For a special scenario, with all four entry approaches being saturated, we model the interactions between entry flow and circulating flow, and prove that the resulting model can be uniquely solved by classic root-finding algorithms. The accuracy of the proposed model is tested with OpenDD, a real-world high-resolution trajectory dataset collected by drones at four roundabouts. The results of the proposed model are shown to consistently outperform the HCM6 model and another gap acceptance-based model.

Suggested Citation

  • Song, Yang & Hu, Xianbiao & Lu, Jiawei & Zhou, Xuesong, 2022. "Analytical approximation and calibration of roundabout capacity: A merging state transition-based modeling approach," Transportation Research Part B: Methodological, Elsevier, vol. 163(C), pages 232-257.
  • Handle: RePEc:eee:transb:v:163:y:2022:i:c:p:232-257
    DOI: 10.1016/j.trb.2022.07.006
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    References listed on IDEAS

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    1. Hagring, Ola, 1998. "A further generalization of Tanner's formula," Transportation Research Part B: Methodological, Elsevier, vol. 32(6), pages 423-429, August.
    2. Fisk, C. S., 1991. "Traffic performance analysis at roundabouts," Transportation Research Part B: Methodological, Elsevier, vol. 25(2-3), pages 89-102.
    3. Andrea Pompigna & Marco Guerrieri & Raffaele Mauro, 2020. "New Extensions and Applications of the Modified Chumanov Model for Calculating Entry Capacity of Single-Lane Roundabouts," Sustainability, MDPI, vol. 12(15), pages 1-21, July.
    4. Bunker, Jonathan & Troutbeck, Rod, 2003. "Prediction of minor stream delays at a limited priority freeway merge," Transportation Research Part B: Methodological, Elsevier, vol. 37(8), pages 719-735, September.
    5. Pollatschek, Moshe A. & Polus, Abishai & Livneh, Moshe, 2002. "A decision model for gap acceptance and capacity at intersections," Transportation Research Part B: Methodological, Elsevier, vol. 36(7), pages 649-663, August.
    6. Wong, S. C., 1996. "On the reserve capacities of priority junctions and roundabouts," Transportation Research Part B: Methodological, Elsevier, vol. 30(6), pages 441-453, December.
    7. Yok Hoe Yap & Helen M. Gibson & Ben J. Waterson, 2013. "An International Review of Roundabout Capacity Modelling," Transport Reviews, Taylor & Francis Journals, vol. 33(5), pages 593-616, September.
    8. Wu, Ning, 2001. "A universal procedure for capacity determination at unsignalized (priority-controlled) intersections," Transportation Research Part B: Methodological, Elsevier, vol. 35(6), pages 593-623, July.
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