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On the minimization of traffic congestion in road networks with tolls

Author

Listed:
  • F. Stefanello

    (Universidade Federal do Rio Grande do Sul)

  • L. S. Buriol

    (Universidade Federal do Rio Grande do Sul)

  • M. J. Hirsch

    (ISEA TEK)

  • P. M. Pardalos

    (University of Florida)

  • T. Querido

    (Linear Options Consulting)

  • M. G. C. Resende

    (Inc.)

  • M. Ritt

    (Universidade Federal do Rio Grande do Sul)

Abstract

Population growth and the massive production of automotive vehicles have lead to the increase of traffic congestion problems. Traffic congestion today is not limited to large metropolitan areas, but is observed even in medium-sized cities and highways. Traffic engineering can contribute to lessen these problems. One possibility, explored in this paper, is to assign tolls to streets and roads, with the objective of inducing drivers to take alternative routes, and thus better distribute traffic across the road network. This assignment problem is often referred to as the tollbooth problem and it is NP-hard. In this paper, we propose mathematical formulations for two versions of the tollbooth problem that use piecewise-linear functions to approximate congestion cost. We also apply a biased random-key genetic algorithm on a set of real-world instances, analyzing solutions when computing shortest paths according to two different weight functions. Experimental results show that the proposed piecewise-linear functions approximate the original convex function quite well and that the biased random-key genetic algorithm produces high-quality solutions.

Suggested Citation

  • F. Stefanello & L. S. Buriol & M. J. Hirsch & P. M. Pardalos & T. Querido & M. G. C. Resende & M. Ritt, 2017. "On the minimization of traffic congestion in road networks with tolls," Annals of Operations Research, Springer, vol. 249(1), pages 119-139, February.
    • Handle: RePEc:spr:annopr:v:249:y:2017:i:1:d:10.1007_s10479-015-1800-1
    DOI: 10.1007/s10479-015-1800-1
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    References listed on IDEAS

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    1. Lihui Bai & Donald Hearn & Siriphong Lawphongpanich, 2010. "A heuristic method for the minimum toll booth problem," Journal of Global Optimization, Springer, vol. 48(4), pages 533-548, December.
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    Cited by:

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    2. Aminu Bello Usman & Jairo Gutierrez, 2019. "DATM: a dynamic attribute trust model for efficient collaborative routing," Annals of Operations Research, Springer, vol. 277(2), pages 293-310, June.
    3. Urmila Pyakurel & Hari Nandan Nath & Tanka Nath Dhamala, 2019. "Partial contraflow with path reversals for evacuation planning," Annals of Operations Research, Springer, vol. 283(1), pages 591-612, December.
    4. Han, Linghui & Zhu, Chengjuan & Wang, David Z.W. & Sun, Huijun & Tan, Zhijia & Meng, Meng, 2019. "Discrete-time dynamic road congestion pricing under stochastic user optimal principle," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 24-36.
    5. André Renato Villela Silva & Luiz Satoru Ochi & Bruno José da Silva Barros & Rian Gabriel S. Pinheiro, 2020. "Efficient approaches for the Flooding Problem on graphs," Annals of Operations Research, Springer, vol. 286(1), pages 33-54, March.
    6. Caio César Freitas & Dario José Aloise & Fábio Francisco Costa Fontes & Andréa Cynthia Santos & Matheus Silva Menezes, 2023. "A biased random-key genetic algorithm for the two-level hub location routing problem with directed tours," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 903-924, September.
    7. Tanzina Afrin & Nita Yodo, 2020. "A Survey of Road Traffic Congestion Measures towards a Sustainable and Resilient Transportation System," Sustainability, MDPI, vol. 12(11), pages 1-23, June.
    8. Coşkun, Safa Bozkurt & Atay, Mehmet Tarık & Şentürk, Erman, 2019. "Interpolated variational iteration method for solving the jamming transition problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 481-493.

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