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Distributions of queue lengths at fixed time traffic signals

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  • Mung, Gregory K. S.
  • Poon, Antonio C. K.
  • Lam, William H. K.

Abstract

This paper presents a new model which studies probability distributions of queue lengths at fixed time traffic signals. It extends Haight's model for Poisson arrivals that the arrival distribution during the effective red period is general and the headway between two successive departures is not less than the minimum departure headway. Moreover, the probability generating function of the queue length, at the end of the effective red period, is derived. The probabilities of the queue lengths, at the ends of the effective green, actual red and amber periods, are also obtained. Comparison is made with Haight's model. Finally a case study for the proposed model is reported.

Suggested Citation

  • Mung, Gregory K. S. & Poon, Antonio C. K. & Lam, William H. K., 1996. "Distributions of queue lengths at fixed time traffic signals," Transportation Research Part B: Methodological, Elsevier, vol. 30(6), pages 421-439, December.
    • Handle: RePEc:eee:transb:v:30:y:1996:i:6:p:421-439
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    References listed on IDEAS

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    1. Heidemann, Dirk, 1994. "Queue length and delay distributions at traffic signals," Transportation Research Part B: Methodological, Elsevier, vol. 28(5), pages 377-389, October.
    2. Katsuhisa Ohno, 1978. "Computational Algorithm for a Fixed Cycle Traffic Signal and New Approximate Expressions for Average Delay," Transportation Science, INFORMS, vol. 12(1), pages 29-47, February.
    3. Richard E. Allsop, 1972. "Delay at a Fixed Time Traffic Signal---I: Theoretical Analysis," Transportation Science, INFORMS, vol. 6(3), pages 260-285, August.
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    Cited by:

    1. Yang, Qiaoli & Shi, Zhongke & Yu, Shaowei & Zhou, Jie, 2018. "Analytical evaluation of the use of left-turn phasing for single left-turn lane only," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 266-303.
    2. Boon, Marko A.A. & van Leeuwaarden, Johan S.H., 2018. "Networks of fixed-cycle intersections," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 254-271.
    3. Comert, Gurcan & Cetin, Mecit, 2009. "Queue length estimation from probe vehicle location and the impacts of sample size," European Journal of Operational Research, Elsevier, vol. 197(1), pages 196-202, August.
    4. Yang, Qiaoli & Shi, Zhongke, 2021. "The queue dynamics of protected/permissive left turns at pre-timed signalized intersections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).
    5. Varga, Balázs & Tettamanti, Tamás & Kulcsár, Balázs & Qu, Xiaobo, 2020. "Public transport trajectory planning with probabilistic guarantees," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 81-101.
    6. Mung, Gregory K. S. & Poon, Antonio C. K. & Lam, William H. K. & Ip, W. C., 1998. "Distribution of the maximum number of opposed turns in a signal cycle at fixed time traffic signals," Transportation Research Part B: Methodological, Elsevier, vol. 32(6), pages 373-386, August.
    7. Yang, Qiaoli & Shi, Zhongke, 2018. "The evolution process of queues at signalized intersections under batch arrivals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 413-425.
    8. Ebben, Mark & van der Zee, Durk-Jouke & van der Heijden, Matthieu, 2004. "Dynamic one-way traffic control in automated transportation systems," Transportation Research Part B: Methodological, Elsevier, vol. 38(5), pages 441-458, June.
    9. Viti, Francesco & van Zuylen, Henk J., 2010. "Probabilistic models for queues at fixed control signals," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 120-135, January.

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