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Queueing at unsignalized intersections

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  • Heidemann, Dirk
  • Wegmann, Helmut

Abstract

A general queueing theory model for traffic flow at unsignalized intersections is described and analysed which contains most of the mathematical models developed in the literature as special cases. Thus a consistent approach is presented for obtaining these models from a general viewpoint. Included are green-red models which are based on an analogy to traffic signals. Critical gaps and merging times or move-up times are allowed to be stochastically dependent. Inconsistent and consistent driver behaviour is considered. Platooning of the major road traffic with random intra-bunch headways is included. The results focus on the distributions of queue lengths and delays and, in particular, on capacities. A general capacity formula is developed and it is shown how the various capacity formulas from the literature come out as special cases. Some numerical results are presented.

Suggested Citation

  • Heidemann, Dirk & Wegmann, Helmut, 1997. "Queueing at unsignalized intersections," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 239-263, June.
    • Handle: RePEc:eee:transb:v:31:y:1997:i:3:p:239-263
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    References listed on IDEAS

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    1. R. J. Troutbeck, 1986. "Average Delay at an Unsignalized Intersection with Two Major Streams Each Having a Dichotomized Headway Distribution," Transportation Science, INFORMS, vol. 20(4), pages 272-286, November.
    2. Fisk, C. S. & Tan, H. H., 1989. "Delay analysis for priority intersections," Transportation Research Part B: Methodological, Elsevier, vol. 23(6), pages 453-469, December.
    3. Heidemann, Dirk, 1991. "Queue length and waiting-time distributions at priority intersections," Transportation Research Part B: Methodological, Elsevier, vol. 25(4), pages 163-174, August.
    4. 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.
    5. 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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    5. Chevallier, Estelle & Leclercq, Ludovic, 2007. "A macroscopic theory for unsignalized intersections," Transportation Research Part B: Methodological, Elsevier, vol. 41(10), pages 1139-1150, December.
    6. 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.
    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.
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    9. Zheng, Yinan & Elefteriadou, Lily, 2017. "A model of pedestrian delay at unsignalized intersections in urban networks," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 138-155.

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