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Generalized gap acceptance models for unsignalized intersections

Author

Listed:
  • Abhishek

    (University of Amsterdam)

  • Marko A. A. Boon

    (Eindhoven University of Technology)

  • Michel Mandjes

    (University of Amsterdam)

Abstract

This paper contributes to the modeling and analysis of unsignalized intersections. In classical gap acceptance models vehicles on the minor road accept any gap greater than the critical gap, and reject gaps below this threshold, where the gap is the time between two subsequent vehicles on the major road. The main contribution of this paper is to develop a series of generalizations of existing models, thus increasing the model’s practical applicability significantly. First, we incorporate driver impatience behavior while allowing for a realistic merging behavior; we do so by distinguishing between the critical gap and the merging time, thus allowing multiple vehicles to use a sufficiently large gap. Incorporating this feature is particularly challenging in models with driver impatience. Secondly, we allow for multiple classes of gap acceptance behavior, enabling us to distinguish between different driver types and/or different vehicle types. Thirdly, we use the novel M $$^X$$ X /SM2/1 queueing model, which has batch arrivals, dependent service times, and a different service-time distribution for vehicles arriving in an empty queue on the minor road (where ‘service time’ refers to the time required to find a sufficiently large gap). This setup facilitates the analysis of the service-time distribution of an arbitrary vehicle on the minor road and of the queue length on the minor road. In particular, we can compute the mean service time, thus enabling the evaluation of the capacity for the minor road vehicles.

Suggested Citation

  • Abhishek & Marko A. A. Boon & Michel Mandjes, 2019. "Generalized gap acceptance models for unsignalized intersections," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(3), pages 385-409, June.
  • Handle: RePEc:spr:mathme:v:89:y:2019:i:3:d:10.1007_s00186-019-00662-0
    DOI: 10.1007/s00186-019-00662-0
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    References listed on IDEAS

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    1. D. P. Gaver, 1963. "A comparison of queue disciplines when service orientation times occur," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 10(1), pages 219-235, March.
    2. George H. Weiss & Alexei A. Maradudin, 1962. "Some Problems in Traffic Delay," Operations Research, INFORMS, vol. 10(1), pages 74-104, February.
    3. Carlos F. Daganzo, 1977. "Traffic Delay at Unsignalized Intersections: Clarification of Some Issues," Transportation Science, INFORMS, vol. 11(2), pages 180-189, May.
    4. de Smit, J. H. A., 1986. "The single server semi-markov queue," Stochastic Processes and their Applications, Elsevier, vol. 22(1), pages 37-50, May.
    5. Heidemann, Dirk, 1994. "Queue length and delay distributions at traffic signals," Transportation Research Part B: Methodological, Elsevier, vol. 28(5), pages 377-389, October.
    6. Abhishek & Marko A. A. Boon & Onno J. Boxma & Rudesindo Núñez-Queija, 2017. "A single-server queue with batch arrivals and semi-Markov services," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 217-240, August.
    7. Abhishek, & Boon, Marko A.A. & Mandjes, Michel & Núñez-Queija, Rudesindo, 2019. "Congestion analysis of unsignalized intersections: The impact of impatience and Markov platooning," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1026-1035.
    8. Catchpole, E. A. & Plank, A. W., 1986. "The capacity of a priority intersection," Transportation Research Part B: Methodological, Elsevier, vol. 20(6), pages 441-456, December.
    9. Heidemann, Dirk & Wegmann, Helmut, 1997. "Queueing at unsignalized intersections," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 239-263, June.
    10. 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.
    11. Cheng, T. C. E. & Allam, S., 1992. "A review of stochastic modelling of delay and capacity at unsignalized priority intersections," European Journal of Operational Research, Elsevier, vol. 60(3), pages 247-259, August.
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    Cited by:

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    2. Arshad Jamal & Muhammad Ijaz & Meshal Almosageah & Hassan M. Al-Ahmadi & Muhammad Zahid & Irfan Ullah & Rabia Emhamed Al Mamlook, 2022. "Implementing the Maximum Likelihood Method for Critical Gap Estimation under Heterogeneous Traffic Conditions," Sustainability, MDPI, vol. 14(23), pages 1-13, November.

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