IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v505y2018icp413-425.html
   My bibliography  Save this article

The evolution process of queues at signalized intersections under batch arrivals

Author

Listed:
  • Yang, Qiaoli
  • Shi, Zhongke

Abstract

The randomness of queue formation and dissipation at signalized intersections is a very important feature of traffic phenomenon, which can be directly reflected by the dynamics and randomness of queue length during a signal cycle. Focusing on the dynamic nature and uncertainty of queues at signalized intersections, a random queueing model with vacations for queues on the multilane is constructed. In particular, the periodic unavailability of signalized intersection and the queue length transitions during a cycle are explicitly taken into account under batch arrival pattern. The steady-state distributions of the queue length along with the time within one cycle on multilane are derived. With it, the effects of batch arrival characteristics of vehicles on the evolution of queue formation and dissipation at signalized intersections are fully captured. The analytical model is compared with Webster’s formula and is further validated with field data, which show that the proposed queueing model is capable of providing a reliable estimation on the queue length In addition, numerical experiments are also conducted to clarify how the queueing process along with the time is affected by different batch arrival patterns, traffic demands, and signal timing, etc.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:413-425
    DOI: 10.1016/j.physa.2018.03.059
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118303790
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.03.059?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Yu, Shaowei & Shi, Zhongke, 2014. "An extended car-following model at signalized intersections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 152-159.
    3. Ge, Hong-Xia & Zheng, Peng-jun & Wang, Wei & Cheng, Rong-Jun, 2015. "The car following model considering traffic jerk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 274-278.
    4. Ou, Hui & Tang, Tie-Qiao, 2018. "An extended two-lane car-following model accounting for inter-vehicle communication," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 260-268.
    5. Jin, Yanfei & Xu, Meng, 2016. "Stability analysis in a car-following model with reaction-time delay and delayed feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 459(C), pages 107-116.
    6. Tang, Tie-Qiao & Zhang, Jian & Liu, Kai, 2017. "A speed guidance model accounting for the driver’s bounded rationality at a signalized intersection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 45-52.
    7. 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.
    8. Chen, Chen & Chen, Jianqiao & Guo, Xiwei, 2010. "Influences of overtaking on two-lane traffic with signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 141-148.
    9. Heidemann, Dirk, 1994. "Queue length and delay distributions at traffic signals," Transportation Research Part B: Methodological, Elsevier, vol. 28(5), pages 377-389, October.
    10. Tang, Jinjun & Zhang, Shen & Chen, Xinqiang & Liu, Fang & Zou, Yajie, 2018. "Taxi trips distribution modeling based on Entropy-Maximizing theory: A case study in Harbin city—China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 430-443.
    11. Zhu, Wen-Xing & Zhang, Li-Dong, 2016. "Analysis of car-following model with cascade compensation strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 265-274.
    12. Nagatani, Takashi, 2009. "Traffic states and fundamental diagram in cellular automaton model of vehicular traffic controlled by signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1673-1681.
    13. Tang, Tie-Qiao & Huang, Hai-Jun & Shang, Hua-Yan, 2017. "An extended macro traffic flow model accounting for the driver’s bounded rationality and numerical tests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 322-333.
    14. Tang, Tie-Qiao & Yi, Zhi-Yan & Lin, Qing-Feng, 2017. "Effects of signal light on the fuel consumption and emissions under car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 200-205.
    15. Hao, Peng & Ban, Xuegang (Jeff) & Guo, Dong & Ji, Qiang, 2014. "Cycle-by-cycle intersection queue length distribution estimation using sample travel times," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 185-204.
    16. Tang, Jinjun & Liu, Fang & Zhang, Weibin & Zhang, Shen & Wang, Yinhai, 2016. "Exploring dynamic property of traffic flow time series in multi-states based on complex networks: Phase space reconstruction versus visibility graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 635-648.
    17. Cheng, Rongjun & Ge, Hongxia & Wang, Jufeng, 2017. "KdV–Burgers equation in a new continuum model based on full velocity difference model considering anticipation effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 52-59.
    18. Tang, Tie-Qiao & Chen, Liang & Wu, Yong-Hong & Caccetta, Lou, 2015. "A macro traffic flow model accounting for real-time traffic state," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 55-67.
    19. Tang, Tie-Qiao & Shao, Yi-Xiao & Chen, Liang, 2017. "Modeling pedestrian movement at the hall of high-speed railway station during the check-in process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 157-166.
    20. Zhang, Shen & Tang, Jinjun & Wang, Haixiao & Wang, Yinhai & An, Shi, 2017. "Revealing intra-urban travel patterns and service ranges from taxi trajectories," Journal of Transport Geography, Elsevier, vol. 61(C), pages 72-86.
    21. 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.
    22. Attahiru Sule Alfa & Marcel F. Neuts, 1995. "Modelling Vehicular Traffic Using the Discrete Time Markovian Arrival Process," Transportation Science, INFORMS, vol. 29(2), pages 109-117, May.
    23. Jiang, Rui & Hu, Mao-Bin & Zhang, H.M. & Gao, Zi-You & Jia, Bin & Wu, Qing-Song, 2015. "On some experimental features of car-following behavior and how to model them," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 338-354.
    24. Zhao, Jing & Li, Peng, 2016. "An extended car-following model with consideration of speed guidance at intersections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 1-8.
    25. M. S. van den Broek & J. S. H. van Leeuwaarden & I. J. B. F. Adan & O. J. Boxma, 2006. "Bounds and Approximations for the Fixed-Cycle Traffic-Light Queue," Transportation Science, INFORMS, vol. 40(4), pages 484-496, November.
    26. Jinjun Tang & Shen Zhang & Yajie Zou & Fang Liu, 2017. "An adaptive map-matching algorithm based on hierarchical fuzzy system from vehicular GPS data," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-11, December.
    27. Tang, Tie-Qiao & Luo, Xiao-Feng & Zhang, Jian & Chen, Liang, 2018. "Modeling electric bicycle’s lane-changing and retrograde behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1377-1386.
    28. Tang, Jinjun & Wang, Yinhai & Wang, Hua & Zhang, Shen & Liu, Fang, 2014. "Dynamic analysis of traffic time series at different temporal scales: A complex networks approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 303-315.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Liu, Zhaoze & Ge, Hongxia & Cheng, Rongjun, 2018. "KdV–Burgers equation in the modified continuum model considering the effect of friction and radius on a curved road," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1218-1227.
    3. Zhaoze, Liu & Rongjun, Cheng & Hongxia, Ge, 2019. "Research on preceding vehicle’s taillight effect and energy consumption in an extended macro traffic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 304-314.
    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. Qi, Xinyue & Ge, Hongxia & Cheng, Rongjun, 2019. "Analysis of a novel lattice hydrodynamic model considering density integral and “backward looking” effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 714-723.
    6. Yongjiang-Wang, & Han-Song, & Rongjun-Cheng,, 2019. "TDGL and mKdV equations for an extended car-following model with the consideration of driver’s memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 440-449.
    7. Chen, Can & Ge, Hongxia & Cheng, Rongjun, 2019. "Self-stabilizing analysis of an extended car-following model with consideration of expected effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    8. Chang, Yinyin & He, Zhiting & Cheng, Rongjun, 2019. "Analysis of the historical time integral form of relative flux and feedback control in an extended lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 326-334.
    9. Jiao, Yulei & Ge, Hongxia & Cheng, Rongjun, 2019. "Nonlinear analysis for a modified continuum model considering electronic throttle (ET) and backward looking effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    10. Rongjun, Cheng & Hongxia, Ge & Jufeng, Wang, 2018. "The nonlinear analysis for a new continuum model considering anticipation and traffic jerk effect," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 493-505.
    11. Jin, Zhizhan & Li, Zhipeng & Cheng, Rongjun & Ge, Hongxia, 2018. "Nonlinear analysis for an improved car-following model account for the optimal velocity changes with memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 278-288.
    12. Chen, Can & Cheng, Rongjun & Ge, Hongxia, 2019. "An extended car-following model considering driver’s sensory memory and the backward looking effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 278-289.
    13. Ma, Xinjuan & Ge, Hongxia & Cheng, Rongjun, 2019. "Influences of acceleration with memory on stability of traffic flow and vehicle’s fuel consumption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 143-154.
    14. Xin, Qi & Fu, Rui & Yuan, Wei & Liu, Qingling & Yu, Shaowei, 2018. "Predictive intelligent driver model for eco-driving using upcoming traffic signal information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 806-823.
    15. Yan, Chunyue & Ge, Hongxia & Cheng, Rongjun, 2019. "An extended car-following model by considering the optimal velocity difference and electronic throttle angle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    16. Wang, Jufeng & Sun, Fengxin & Cheng, Rongjun & Ge, Hongxia, 2018. "An extended car-following model considering the self-stabilizing driving behavior of headway," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 347-357.
    17. Li, Shihao & Cheng, Rongjun & Ge, Hongxia, 2020. "An improved car-following model considering electronic throttle dynamics and delayed velocity difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    18. Jin, Zhizhan & Yang, Zaili & Ge, Hongxia, 2018. "Energy consumption investigation for a new car-following model considering driver’s memory and average speed of the vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 1038-1049.
    19. Wang, Qingying & Ge, Hongxia, 2019. "An improved lattice hydrodynamic model accounting for the effect of “backward looking” and flow integral," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 438-446.
    20. Li, Lixiang & Cheng, Rongjun & Ge, Hongxia, 2021. "New feedback control for a novel two-dimensional lattice hydrodynamic model considering driver’s memory effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:413-425. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.