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Relaxation Algorithms for the General Asymmetric Traffic Equilibrium Problem

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  • Stella Dafermos

    (Brown University, Providence, Rhode Island)

Abstract

In this paper we establish the convergence of two relaxation algorithms designed to solve, respectively, the extended single-mode and the general multimodal network equilibrium problems. Both algorithms are shown to converge linearly; the first under the assumption that the cost functions are not too asymmetric; the second under the assumption that the cost interaction among the different modes is relatively weak.

Suggested Citation

  • Stella Dafermos, 1982. "Relaxation Algorithms for the General Asymmetric Traffic Equilibrium Problem," Transportation Science, INFORMS, vol. 16(2), pages 231-240, May.
    • Handle: RePEc:inm:ortrsc:v:16:y:1982:i:2:p:231-240
    DOI: 10.1287/trsc.16.2.231
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    Cited by:

    1. Louis de Grange & Juan Carlos Muñoz, 2007. "An equivalent optimization formulation for the traffic assignment problem with asymmetric linear costs," Transportation Planning and Technology, Taylor & Francis Journals, vol. 32(1), pages 1-25, March.
    2. D’Acierno, Luca & Gallo, Mariano & Montella, Bruno, 2012. "An Ant Colony Optimisation algorithm for solving the asymmetric traffic assignment problem," European Journal of Operational Research, Elsevier, vol. 217(2), pages 459-469.
    3. Han, Sangjin, 2007. "A route-based solution algorithm for dynamic user equilibrium assignments," Transportation Research Part B: Methodological, Elsevier, vol. 41(10), pages 1094-1113, December.
    4. Castillo González, Rodrigo & Clempner, Julio B. & Poznyak, Alexander S., 2019. "Solving traffic queues at controlled-signalized intersections in continuous-time Markov games," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 283-297.
    5. Han, S. & Heydecker, B.G., 2006. "Consistent objectives and solution of dynamic user equilibrium models," Transportation Research Part B: Methodological, Elsevier, vol. 40(1), pages 16-34, January.
    6. Elnaz Miandoabchi & Reza Farahani & Wout Dullaert & W. Szeto, 2012. "Hybrid Evolutionary Metaheuristics for Concurrent Multi-Objective Design of Urban Road and Public Transit Networks," Networks and Spatial Economics, Springer, vol. 12(3), pages 441-480, September.
    7. Joaquín De Cea & J. Enrique Fernández & Valérie Dekock & Alexandra Soto, 2004. "Solving network equilibrium problems on multimodal urban transportation networks with multiple user classes," Transport Reviews, Taylor & Francis Journals, vol. 25(3), pages 293-317, January.
    8. Vo, Khoa D. & Lam, William H.K. & Chen, Anthony & Shao, Hu, 2020. "A household optimum utility approach for modeling joint activity-travel choices in congested road networks," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 93-125.
    9. Meneguzzer, Claudio, 1995. "An equilibrium route choice model with explicit treatment of the effect of intersections," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 329-356, October.
    10. Dulce Rosas & Jordi Castro & Lídia Montero, 2009. "Using ACCPM in a simplicial decomposition algorithm for the traffic assignment problem," Computational Optimization and Applications, Springer, vol. 44(2), pages 289-313, November.
    11. D E Boyce, 1984. "Urban Transportation Network-Equilibrium and Design Models: Recent Achievements and Future Prospects," Environment and Planning A, , vol. 16(11), pages 1445-1474, November.
    12. Ennio Cascetta & Mariano Gallo & Bruno Montella, 2006. "Models and algorithms for the optimization of signal settings on urban networks with stochastic assignment models," Annals of Operations Research, Springer, vol. 144(1), pages 301-328, April.

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