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Optimizing Traffic Light Green Duration under Stochastic Considerations

Author

Listed:
  • Krasimira Stoilova

    (Institute of Information and Communication Technologies-Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria)

  • Todor Stoilov

    (Institute of Information and Communication Technologies-Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria)

Abstract

An optimization model for traffic light control in an urban network of intersections is derived. The model is based on store-and-forward analytic relations, which account for the length of the queue of waiting vehicles in front of the traffic light intersection. The model is complicated with probabilistic relations that formalize the requirements for maintaining short queues of vehicles. Probabilistic inequalities apply to each intersection of the city network. Approximations of probability inequalities are given in the article. Quadratic deterministic inequalities, which are part of the set of the traffic flow control optimization problem, are derived. Numerical simulations are performed, applying mean estimated data for real traffic in an urban area of Sofia. The model predictive approach is applied to traffic light optimization and control. Empirical results give advantages of the obtained model compared to the classical store-and-forward optimization model for the total number of vehicles waiting in the considered urban network.

Suggested Citation

  • Krasimira Stoilova & Todor Stoilov, 2023. "Optimizing Traffic Light Green Duration under Stochastic Considerations," Mathematics, MDPI, vol. 11(3), pages 1-25, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:496-:d:1038282
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    References listed on IDEAS

    as
    1. Chi-kwong Wong & Yiu-yin Lee, 2020. "Lane-Based Traffic Signal Simulation and Optimization for Preventing Overflow," Mathematics, MDPI, vol. 8(8), pages 1-28, August.
    2. Wei Huang & Yang Hu & Xuanyu Zhang, 2022. "Enhancing Model-Based Anticipatory Traffic Signal Control with Metamodeling and Adaptive Optimization," Mathematics, MDPI, vol. 10(15), pages 1-18, July.
    3. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    4. Yin, Yafeng, 2008. "Robust optimal traffic signal timing," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 911-924, December.
    5. Yona Elbaum & Alexander Novoselsky & Evgeny Kagan, 2022. "A Queueing Model for Traffic Flow Control in the Road Intersection," Mathematics, MDPI, vol. 10(21), pages 1-15, October.
    6. Krešimir Kušić & Edouard Ivanjko & Filip Vrbanić & Martin Gregurić & Ivana Dusparic, 2021. "Spatial-Temporal Traffic Flow Control on Motorways Using Distributed Multi-Agent Reinforcement Learning," Mathematics, MDPI, vol. 9(23), pages 1-28, November.
    7. Ismail Shah & Izhar Muhammad & Sajid Ali & Saira Ahmed & Mohammed M. A. Almazah & A. Y. Al-Rezami, 2022. "Forecasting Day-Ahead Traffic Flow Using Functional Time Series Approach," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
    8. Vladimir Shepelev & Alexandr Glushkov & Olga Fadina & Aleksandr Gritsenko, 2022. "Comparative Evaluation of Road Vehicle Emissions at Urban Intersections with Detailed Traffic Dynamics," Mathematics, MDPI, vol. 10(11), pages 1-19, May.
    9. Sadiqa Jafari & Zeinab Shahbazi & Yung-Cheol Byun, 2022. "Improving the Road and Traffic Control Prediction Based on Fuzzy Logic Approach in Multiple Intersections," Mathematics, MDPI, vol. 10(16), pages 1-16, August.
    10. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    11. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    12. Mehran Amini & Miklos F. Hatwagner & Laszlo T. Koczy, 2022. "A Combined Approach of Fuzzy Cognitive Maps and Fuzzy Rule-Based Inference Supporting Freeway Traffic Control Strategies," Mathematics, MDPI, vol. 10(21), pages 1-17, November.
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