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Queues for a Vehicle-Actuated Traffic Light

Author

Listed:
  • J. N. Darroch

    (Mathematics Department, University of Adelaide, South Australia)

  • G. F. Newell

    (Mathematics Department, University of Adelaide, South Australia)

  • R. W. J. Morris

    (Traffic Engineering Branch, South Australia Highways and Local Government Department)

Abstract

A vehicle-actuated traffic light controls two intersecting traffic streams keeping the light green for lane i , i = 1 or 2 until any existing queue has been discharged and a headway of duration at least β ı , is detected in the subsequent arrivals. The object of this paper is to investigate how one should choose the β i so as to minimize the average delay per vehicle at the intersection. A model is considered in which the arrival headways are exponentially distributed random variables, departure headways have any specified distribution, and there is a random lost time for each switch of the traffic light. Formulas are derived for the moments of the cycle times, the average wait per vehicle, and the optimal β i .

Suggested Citation

  • J. N. Darroch & G. F. Newell & R. W. J. Morris, 1964. "Queues for a Vehicle-Actuated Traffic Light," Operations Research, INFORMS, vol. 12(6), pages 882-895, December.
    • Handle: RePEc:inm:oropre:v:12:y:1964:i:6:p:882-895
    DOI: 10.1287/opre.12.6.882
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    Citations

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    Cited by:

    1. Pedro Cesar Lopes Gerum & Andrew Reed Benton & Melike Baykal-Gürsoy, 2019. "Traffic density on corridors subject to incidents: models for long-term congestion management," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(5), pages 795-831, December.
    2. 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).
    3. Boon, Marko & Janssen, Guido & van Leeuwaarden, Johan & Timmerman, Rik, 2023. "Optimal capacity allocation for heavy-traffic fixed-cycle traffic-light queues and intersections," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 79-98.
    4. Baykal-Gürsoy, M. & Xiao, W. & Ozbay, K., 2009. "Modeling traffic flow interrupted by incidents," European Journal of Operational Research, Elsevier, vol. 195(1), pages 127-138, May.
    5. Recker, Will, 2008. "Development of an Adaptive Corridor Traffic Control Model," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt1sq7049f, Institute of Transportation Studies, UC Berkeley.
    6. Recker, Will & Zhenhg, Xing & Chu, Lianyu, 2010. "Development of an Adaptive Corridor Traffic Control Model," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3tx5b17h, Institute of Transportation Studies, UC Berkeley.
    7. A. Oblakova & A. Al Hanbali & R. J. Boucherie & J. C. W. Ommeren & W. H. M. Zijm, 2019. "An exact root-free method for the expected queue length for a class of discrete-time queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 92(3), pages 257-292, August.
    8. Tae Son, Young, 1999. "Queueing delay models for two-lane highway work zones," Transportation Research Part B: Methodological, Elsevier, vol. 33(7), pages 459-471, September.
    9. 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.

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