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The convergence of diagonalization algorithms for asymmetric network equilibrium problems

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  • Florian, Michael
  • Spiess, Heinz

Abstract

We provide a sufficient condition for the convergence of diagonalization algorithms for equilibrium traffic assignment problems with asymmetric Jacobian matrix B(v) of the link user cost mapping s(v) of the flow v. When , where D(v*) > 0 is the diagonal of B(v*) and v* is the equilibrium flow, we demonstrate a local convergence theorem for nonlinear cost functions. The implication of this result for practical applications of the model are outlined.

Suggested Citation

  • Florian, Michael & Spiess, Heinz, 1982. "The convergence of diagonalization algorithms for asymmetric network equilibrium problems," Transportation Research Part B: Methodological, Elsevier, vol. 16(6), pages 477-483, December.
    • Handle: RePEc:eee:transb:v:16:y:1982:i:6:p:477-483
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    Cited by:

    1. Moore, II, James E. & Kim, Geunyoung & Cho, Seongdil & Hu, Hsi-hwa & Xu, Rong, 1997. "Evaluating System ATMIS Technologies Via Rapid Estimation Of Network Flows: Final Report," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt5c70f3d9, Institute of Transportation Studies, UC Berkeley.
    2. Zhou, Zhong & Chen, Anthony & Wong, S.C., 2009. "Alternative formulations of a combined trip generation, trip distribution, modal split, and trip assignment model," European Journal of Operational Research, Elsevier, vol. 198(1), pages 129-138, October.
    3. 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.
    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. Tadashi Yamada & Bona Frazila Russ & Jun Castro & Eiichi Taniguchi, 2009. "Designing Multimodal Freight Transport Networks: A Heuristic Approach and Applications," Transportation Science, INFORMS, vol. 43(2), pages 129-143, May.
    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. Mohamad K. Hasan & Mohammad Saoud & Raed Al-Husain, 2021. "Supernetwork Representation Formulation of a Multiclass Simultaneous Transportation Equilibrium Model as a Fixed Demand User Equilibrium Problem," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 12(3), pages 18-33, July.
    8. 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.
    9. Patrice Marcotte & Laura Wynter, 2004. "A New Look at the Multiclass Network Equilibrium Problem," Transportation Science, INFORMS, vol. 38(3), pages 282-292, August.
    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. Mohamad Hasan & Hussain Dashti, 2007. "A Multiclass Simultaneous Transportation Equilibrium Model," Networks and Spatial Economics, Springer, vol. 7(3), pages 197-211, September.
    13. Li, Guoyuan & Chen, Anthony, 2023. "Strategy-based transit stochastic user equilibrium model with capacity and number-of-transfers constraints," European Journal of Operational Research, Elsevier, vol. 305(1), pages 164-183.
    14. 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.
    15. Frédéric Meunier & Thomas Pradeau, 2019. "Computing solutions of the multiclass network equilibrium problem with affine cost functions," Annals of Operations Research, Springer, vol. 274(1), pages 447-469, March.

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