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Queue length and delay distributions at traffic signals

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  • Heidemann, Dirk

Abstract

Some new analytical results on statistical distributions of queue lenghts and delays at traffic signals are derived. For this purpose, the probability generating function of the queue length distribution is developed, from which the Laplace-transform of the delay distribution is obtained. A Poisson arrival process and fixed-time control are assumed. Similar techniques have successfully been employed to obtain the queue-length and delay distributions at priority intersections. Thus, a unified theory for both signalized and unsignalized intersections results.

Suggested Citation

  • Heidemann, Dirk, 1994. "Queue length and delay distributions at traffic signals," Transportation Research Part B: Methodological, Elsevier, vol. 28(5), pages 377-389, October.
    • Handle: RePEc:eee:transb:v:28:y:1994:i:5:p:377-389
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    1. Comert, Gurcan, 2016. "Queue length estimation from probe vehicles at isolated intersections: Estimators for primary parameters," European Journal of Operational Research, Elsevier, vol. 252(2), pages 502-521.
    2. Osorio, Carolina & Wang, Carter, 2017. "On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 305-339.
    3. Gao, Yuhong & Qu, Zhaowei & Song, Xianmin & Yun, Zhenyu & Xia, Yingji, 2021. "A novel relationship model between signal timing, queue length and travel speed," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    4. 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.
    5. Omid, M. Rouhani, 2013. "Queue Dissipation Shockwave Speed for Signalized Intersections," MPRA Paper 53161, University Library of Munich, Germany.
    6. Sara Sasaninejad & Joris Van Malderen & Joris Walraevens & Sabine Wittevrongel, 2023. "Expected Waiting Times at an Intersection with a Green Extension Strategy for Freight Vehicles: An Analytical Analysis," Mathematics, MDPI, vol. 11(3), pages 1-26, February.
    7. Yang, Qiaoli & Shi, Zhongke & Tang, Min-an & Gao, Fengyang & Yu, Shaowei, 2019. "Modeling the permissive-only left-turn queue at signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 315-325.
    8. 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.
    9. 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.
    10. 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.
    11. 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).
    12. 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.
    13. Osorio, Carolina & Flötteröd, Gunnar & Bierlaire, Michel, 2011. "Dynamic network loading: A stochastic differentiable model that derives link state distributions," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1410-1423.
    14. Yang, Qiaoli & Shi, Zhongke, 2018. "Effects of the design of waiting areas on the dynamic behavior of queues at signalized intersections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 181-195.
    15. Rouhani, Omid M., 2013. "Queue Dissipation Shockwave Speed– A Signalized Intersection Case Study," 54th Annual Transportation Research Forum, Annapolis, Maryland, March 21-23, 2013 206954, Transportation Research Forum.
    16. António Pacheco & Maria Lurdes Simões Simões & Paula Milheiro-Oliveira, 2017. "Queues with Server Vacations as a Model for Pretimed Signalized Urban Traffic," Transportation Science, INFORMS, vol. 51(3), pages 841-851, August.
    17. Yang, Qiaoli & He, Yongzhen, 2022. "Right-turn-on-red queueing process at signalized intersections with a short right-turn lane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    18. 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.
    19. J. S. H. van Leeuwaarden, 2006. "Delay Analysis for the Fixed-Cycle Traffic-Light Queue," Transportation Science, INFORMS, vol. 40(2), pages 189-199, May.
    20. 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.
    21. Dion, Francois & Rakha, Hesham & Kang, Youn-Soo, 2004. "Comparison of delay estimates at under-saturated and over-saturated pre-timed signalized intersections," Transportation Research Part B: Methodological, Elsevier, vol. 38(2), pages 99-122, February.
    22. Yang, Qiaoli & Deng, Kang & Gao, Fengyang & Yu, Shaowei & Dou, Zufang & Zhang, Tingrong, 2022. "Characterizing the dynamics and uncertainty of queues at signalized intersections with left-turn bay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    23. 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.
    24. 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.
    25. Yang, Qiaoli & Fu, Xue, 2024. "An extended queueing model for vehicles at signalized intersections considering the platoon correlated arrivals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 635(C).

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