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The Holding Problem with Real–Time Information Available

Author

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  • Xu Jun Eberlein

    (Caliper Corporation, Newton, Massachusetts 02161)

  • Nigel H. M. Wilson

    (Department of Civil and Environment Engineering, MIT, Cambridge, Massachusetts 02139)

  • David Bernstein

    (Department of Computer Science, James Madison University, Harrisonburg, VA 22807)

Abstract

Holding is one of the most commonly used real–time control strategies in transit operations. Given a transit network and its operations plan, the holding problem is to decide at a given time at a control station, which vehicle is to be held and for how long, such that the total passenger cost along the route is minimized over a time period. Previous research on the holding problem has always assumed no real–time information available. Such an assumption not only poses great difficulties in solving the problem, but also limits practical applications in a real–time, dynamic operations environment. In this paper we formulate the holding problem as a deterministic quadratic program in a rolling horizon scheme, and develop an efficient solution algorithm to solve it. Using headway data collected by an automated system, we tested the algorithm and evaluated the impact of the resulting holding policies. Important and interesting properties of the holding solution, obtained from both theoretical and computational analyses, are presented.

Suggested Citation

  • Xu Jun Eberlein & Nigel H. M. Wilson & David Bernstein, 2001. "The Holding Problem with Real–Time Information Available," Transportation Science, INFORMS, vol. 35(1), pages 1-18, February.
    • Handle: RePEc:inm:ortrsc:v:35:y:2001:i:1:p:1-18
    DOI: 10.1287/trsc.35.1.1.10143
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    References listed on IDEAS

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    1. Warren B. Powell, 1985. "Analysis of Vehicle Holding and Cancellation Strategies in Bulk Arrival, Bulk Service Queues," Transportation Science, INFORMS, vol. 19(4), pages 352-377, November.
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    Cited by:

    1. Federico Malucelli & Emanuele Tresoldi, 2019. "Delay and disruption management in local public transportation via real-time vehicle and crew re-scheduling: a case study," Public Transport, Springer, vol. 11(1), pages 1-25, June.
    2. Wu, Weitiao & Liu, Ronghui & Jin, Wenzhou, 2016. "Designing robust schedule coordination scheme for transit networks with safety control margins," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 495-519.
    3. Zhang, Shuyang & Lo, Hong K., 2018. "Two-way-looking self-equalizing headway control for bus operations," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 280-301.
    4. Schmöcker, Jan-Dirk & Sun, Wenzhe & Fonzone, Achille & Liu, Ronghui, 2016. "Bus bunching along a corridor served by two lines," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 300-317.
    5. Petit, Antoine & Ouyang, Yanfeng & Lei, Chao, 2018. "Dynamic bus substitution strategy for bunching intervention," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 1-16.
    6. Daganzo, Carlos F. & Pilachowski, Josh, 2009. "Reducing bunching with bus-to-bus cooperation," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt0551g0zw, Institute of Transportation Studies, UC Berkeley.
    7. Wu, Weitiao & Liu, Ronghui & Jin, Wenzhou, 2017. "Modelling bus bunching and holding control with vehicle overtaking and distributed passenger boarding behaviour," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 175-197.
    8. Sirmatel, Isik Ilber & Geroliminis, Nikolas, 2018. "Mixed logical dynamical modeling and hybrid model predictive control of public transport operations," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 325-345.
    9. Li, Shukai & Dessouky, Maged M. & Yang, Lixing & Gao, Ziyou, 2017. "Joint optimal train regulation and passenger flow control strategy for high-frequency metro lines," Transportation Research Part B: Methodological, Elsevier, vol. 99(C), pages 113-137.
    10. Li, Shukai & Zhou, Xuesong & Yang, Lixing & Gao, Ziyou, 2018. "Automatic train regulation of complex metro networks with transfer coordination constraints: A distributed optimal control framework," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 228-253.
    11. David Verbich & Ehab Diab & Ahmed El-Geneidy, 2016. "Have they bunched yet? An exploratory study of the impacts of bus bunching on dwell and running times," Public Transport, Springer, vol. 8(2), pages 225-242, September.
    12. Dai, Zhuang & Liu, Xiaoyue Cathy & Chen, Zhuo & Guo, Renyong & Ma, Xiaolei, 2019. "A predictive headway-based bus-holding strategy with dynamic control point selection: A cooperative game theory approach," Transportation Research Part B: Methodological, Elsevier, vol. 125(C), pages 29-51.
    13. Xuan, Yiguang & Argote, Juan & Daganzo, Carlos F., 2011. "A Dynamic Holding Strategy to Improve Bus ScheduleReliability and Commercial Speed," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt0jp7c8k8, Institute of Transportation Studies, UC Berkeley.
    14. Li, Shukai & Liu, Ronghui & Yang, Lixing & Gao, Ziyou, 2019. "Robust dynamic bus controls considering delay disturbances and passenger demand uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 123(C), pages 88-109.
    15. Wang, Yihui & D’Ariano, Andrea & Yin, Jiateng & Meng, Lingyun & Tang, Tao & Ning, Bin, 2018. "Passenger demand oriented train scheduling and rolling stock circulation planning for an urban rail transit line," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 193-227.
    16. Petit, Antoine & Lei, Chao & Ouyang, Yanfeng, 2019. "Multiline Bus Bunching Control via Vehicle Substitution," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 68-86.
    17. Andres, Matthias & Nair, Rahul, 2017. "A predictive-control framework to address bus bunching," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 123-148.
    18. Wei Wu & Wanjing Ma & Kejun Long & Heping Zhou & Yi Zhang, 2016. "Designing Sustainable Public Transportation: Integrated Optimization of Bus Speed and Holding Time in a Connected Vehicle Environment," Sustainability, MDPI, vol. 8(11), pages 1-15, November.
    19. Gabriel E. Sánchez-Martínez & Nigel H. M. Wilson & Haris N. Koutsopoulos, 2017. "Schedule-free high-frequency transit operations," Public Transport, Springer, vol. 9(1), pages 285-305, July.
    20. Chow, Andy H.F. & Li, Shuai & Zhong, Renxin, 2017. "Multi-objective optimal control formulations for bus service reliability with traffic signals," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 248-268.

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