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Optimization of Traffic Signal Settings by Mixed-Integer Linear Programming

Author

Listed:
  • Nathan H. Gartner

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • John D. C. Little

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Henry Gabbay

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

Setting traffic signals in a signal-controlled street network involves the determination of cycle time, splits of green time, and offsets. Part I of this paper considers the network coordination problem, i.e., given a common cycle lime and green splits at each intersection, determine offsets for all signals. Part II considers the more general synchronization problem, i.e., determine simultaneously all the control variables for the network including offsets, splits, and cycle time. In Part I, a link performance function is developed to express the loss incurred by platoons traveling through a signal-controlled intersection us a function of link offset. Integer variables enter the formulation because of the periodicity of the traffic lights: The algebraic sum of the offsets around any closed loop of the network must equal an integral number of cycle limes. The optimization problem is formulated as a mixed-integer linear program and a test network is solved by branch-and-bound techniques using IBM's MPSX package.

Suggested Citation

  • Nathan H. Gartner & John D. C. Little & Henry Gabbay, 1975. "Optimization of Traffic Signal Settings by Mixed-Integer Linear Programming," Transportation Science, INFORMS, vol. 9(4), pages 321-343, November.
    • Handle: RePEc:inm:ortrsc:v:9:y:1975:i:4:p:321-343
    DOI: 10.1287/trsc.9.4.321
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    Citations

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    Cited by:

    1. Le, Tung & Vu, Hai L. & Walton, Neil & Hoogendoorn, Serge P. & Kovács, Péter & Queija, Rudesindo N., 2017. "Utility optimization framework for a distributed traffic control of urban road networks," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 539-558.
    2. Zhou, Xuesong, 2017. "Recasting and optimizing intersection automation as a connected-and-automated-vehicle (CAV) scheduling problem: A sequential branch-and-bound search approach in phase-time-traffic hypernetworkAuthor-N," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 479-506.
    3. Rey, David & Levin, Michael W., 2019. "Blue phase: Optimal network traffic control for legacy and autonomous vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 130(C), pages 105-129.
    4. Pillai, Rekha S. & Rathi*, Ajay K. & L. Cohen, Stephen, 1998. "A restricted branch-and-bound approach for generating maximum bandwidth signal timing plans for traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 517-529, November.
    5. Yao, Zhihong & Zhao, Bin & Qin, Lingqiao & Jiang, Yangsheng & Ran, Bin & Peng, Bo, 2020. "An efficient heterogeneous platoon dispersion model for real-time traffic signal control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    6. Coogan, Samuel & Kim, Eric & Gomes, Gabriel & Arcak, Murat & Varaiya, Pravin, 2017. "Offset optimization in signalized traffic networks via semidefinite relaxation," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 82-92.
    7. Sadek, Bassel & Doig Godier, Jean & Cassidy, Michael J & Daganzo, Carlos F, 2022. "Traffic signal plans to decongest street grids," Transportation Research Part B: Methodological, Elsevier, vol. 162(C), pages 195-208.
    8. Little, John D. C. & Kelson, Mark D. & Gartner, Nathan H., 1981. "MAXBAND : a versatile program for setting signals on arteries and triangular networks," Working papers 1185-81., Massachusetts Institute of Technology (MIT), Sloan School of Management.

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