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The Synchronization of Traffic Signals by Mixed-Integer Linear Programming

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  • John D. C. Little

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

Traffic signals can be synchronized so that a car, starting at one end of a main artery and traveling at preassigned speeds, can go to the other end without stopping for a red light. The portion of a signal cycle for which this is possible is called the bandwidth for that direction. A mixed-integer linear program is formulated for the following arterial problem: Given (1) an arbitrary number of signals, (2) the red-green split at each signal, (3) upper and lower limits on signal period, (4) upper and lower limits on speed between adjacent signals, and (5) limits on change in speed, find (1) common signal period, (2) speeds between signals, and (3) the relative phasing of the signals, in order to maximize the sum of the bandwidths for the two directions. Several variants of the problem are formulated, including the problem of synchronizing a network of signals. Branch-and-bound algorithms are developed for solving the mixed-integer linear programs by solving sequences of ordinary linear programs. A 10-signal arterial example and a 7-signal network example are worked out.

Suggested Citation

  • John D. C. Little, 1966. "The Synchronization of Traffic Signals by Mixed-Integer Linear Programming," Operations Research, INFORMS, vol. 14(4), pages 568-594, August.
    • Handle: RePEc:inm:oropre:v:14:y:1966:i:4:p:568-594
    DOI: 10.1287/opre.14.4.568
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    Cited by:

    1. Yin, Yafeng, 2008. "Robust optimal traffic signal timing," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 911-924, December.
    2. 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.
    3. Shenzhen Ding & Xumei Chen & Lei Yu & Xu Wang, 2019. "Arterial Offset Optimization Considering the Delay and Emission of Platoon: A Case Study in Beijing," Sustainability, MDPI, vol. 11(14), pages 1-19, July.
    4. Bielli, Maurizio & Reverberi, Pierfrancesco, 1996. "New operations research and artificial intelligence approaches to traffic engineering problems," European Journal of Operational Research, Elsevier, vol. 92(3), pages 550-572, August.
    5. Papola, Natale & Fusco, Gaetano, 1998. "Maximal bandwidth problems: a new algorithm based on the properties of periodicity of the system," Transportation Research Part B: Methodological, Elsevier, vol. 32(4), pages 277-288, May.
    6. Zhou, Hongmin & Hawkins, H. Gene & Zhang, Yunlong, 2017. "Arterial signal coordination with uneven double cycling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 103(C), pages 409-429.

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