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On the equivalence between stationary link flow patterns and traffic network equilibria

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  • Zhang, Ding
  • Nagurney, Anna
  • Wu, Jiahao

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  • Zhang, Ding & Nagurney, Anna & Wu, Jiahao, 2001. "On the equivalence between stationary link flow patterns and traffic network equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 35(8), pages 731-748, September.
    • Handle: RePEc:eee:transb:v:35:y:2001:i:8:p:731-748
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    5. Anna Nagurney & Ding Zhang, 1997. "Projected Dynamical Systems in the Formulation, Stability Analysis, and Computation of Fixed-Demand Traffic Network Equilibria," Transportation Science, INFORMS, vol. 31(2), pages 147-158, May.
    6. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    7. Hani S. Mahmassani & Gang-Len Chang, 1987. "On Boundedly Rational User Equilibrium in Transportation Systems," Transportation Science, INFORMS, vol. 21(2), pages 89-99, May.
    8. D. Zhang & A. Nagurney, 1997. "Formulation, Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 417-444, May.
    9. Watling, David, 1998. "Perturbation stability of the asymmetric stochastic equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 32(3), pages 155-171, April.
    10. Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
    11. Janson, Bruce N., 1991. "Dynamic traffic assignment for urban road networks," Transportation Research Part B: Methodological, Elsevier, vol. 25(2-3), pages 143-161.
    12. Horowitz, Joel L., 1984. "The stability of stochastic equilibrium in a two-link transportation network," Transportation Research Part B: Methodological, Elsevier, vol. 18(1), pages 13-28, February.
    13. Y. W. Xu & J. H. Wu & M. Florian & P. Marcotte & D. L. Zhu, 1999. "Advances in the Continuous Dynamic Network Loading Problem," Transportation Science, INFORMS, vol. 33(4), pages 341-353, November.
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    Cited by:

    1. Wen-yi Zhang & Wei Guan & Ji-hui Ma & Jun-fang Tian, 2015. "A Nonlinear Pairwise Swapping Dynamics to Model the Selfish Rerouting Evolutionary Game," Networks and Spatial Economics, Springer, vol. 15(4), pages 1075-1092, December.
    2. Han, Linghui & Wang, David Z.W. & Lo, Hong K. & Zhu, Chengjuan & Cai, Xingju, 2017. "Discrete-time day-to-day dynamic congestion pricing scheme considering multiple equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 1-16.
    3. Xu, Xiangdong & Qu, Kai & Chen, Anthony & Yang, Chao, 2021. "A new day-to-day dynamic network vulnerability analysis approach with Weibit-based route adjustment process," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 153(C).
    4. Wenyi Zhang & Wei Guan & Jihui Ma & Tao Wang, 2013. "Nonlinear Min-Cost-Pursued Route-Swapping Dynamic System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-10, May.
    5. Ren-Yong Guo & Hai-Jun Huang & Hai Yang, 2019. "Tradable Credit Scheme for Control of Evolutionary Traffic Flows to System Optimum: Model and its Convergence," Networks and Spatial Economics, Springer, vol. 19(3), pages 833-868, September.
    6. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Tan, Zhijia, 2015. "Link-based day-to-day network traffic dynamics and equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 248-260.
    7. Peeta, Srinivas, 2016. "A marginal utility day-to-day traffic evolution model based on one-step strategic thinkingAuthor-Name: He, Xiaozheng," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 237-255.
    8. Iryo, Takamasa, 2019. "Instability of departure time choice problem: A case with replicator dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 353-364.
    9. Kumar, Amit & Peeta, Srinivas, 2015. "A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 235-256.
    10. G. E. Cantarella & D. P. Watling, 2016. "Modelling road traffic assignment as a day-to-day dynamic, deterministic process: a unified approach to discrete- and continuous-time models," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 69-98, March.
    11. Malachy Carey & Y. Ge, 2012. "Comparison of Methods for Path Flow Reassignment for Dynamic User Equilibrium," Networks and Spatial Economics, Springer, vol. 12(3), pages 337-376, September.
    12. Watling, David P., 2016. "A route-swapping dynamical system and Lyapunov function for stochastic user equilibriumAuthor-Name: Smith, Michael J," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 132-141.
    13. Qi, Hang & Jia, Ning & Qu, Xiaobo & He, Zhengbing, 2023. "Investigating day-to-day route choices based on multi-scenario laboratory experiments, Part I: Route-dependent attraction and its modeling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 167(C).
    14. Ye, Hongbo & Xiao, Feng & Yang, Hai, 2021. "Day-to-day dynamics with advanced traveler information," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 23-44.
    15. Ren-Yong Guo & Hai Yang & Hai-Jun Huang & Zhijia Tan, 2016. "Day-to-Day Flow Dynamics and Congestion Control," Transportation Science, INFORMS, vol. 50(3), pages 982-997, August.
    16. Djavadian, Shadi & Chow, Joseph Y.J., 2017. "An agent-based day-to-day adjustment process for modeling ‘Mobility as a Service’ with a two-sided flexible transport market," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 36-57.
    17. Rambha, Tarun & Boyles, Stephen D., 2016. "Dynamic pricing in discrete time stochastic day-to-day route choice models," Transportation Research Part B: Methodological, Elsevier, vol. 92(PA), pages 104-118.
    18. Wang, Guanfeng & Jia, Hongfei & Feng, Tao & Tian, Jingjing & Wu, Ruiyi & Gao, Heyao & Liu, Chao, 2024. "Modelling the dual dynamic traffic flow evolution with information perception differences between human-driven vehicles and connected autonomous vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 640(C).
    19. Yang, Fan & Zhang, Ding, 2009. "Day-to-day stationary link flow pattern," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 119-126, January.
    20. Ding, Hongxing & Yang, Hai & Xu, Hongli & Li, Ting, 2023. "Status quo-dependent user equilibrium model with adaptive value of time," Transportation Research Part B: Methodological, Elsevier, vol. 170(C), pages 77-90.
    21. Anna Nagurney & Dong Li, 2014. "A Dynamic Network Oligopoly Model with Transportation Costs, Product Differentiation, and Quality Competition," Computational Economics, Springer;Society for Computational Economics, vol. 44(2), pages 201-229, August.
    22. Roger B. Chen & Christopher Valant, 2023. "Stability and Convergence in Matching Processes for Shared Mobility Systems," Networks and Spatial Economics, Springer, vol. 23(2), pages 469-486, June.
    23. Liang, Qingnan & Li, Xin-an & Chen, Zhibin & Pan, Tianlu & Zhong, Renxin, 2023. "Day-to-day traffic control for networks mixed with regular human-piloted and connected autonomous vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 178(C).
    24. Hongbo Ye & Hai Yang, 2017. "Rational Behavior Adjustment Process with Boundedly Rational User Equilibrium," Transportation Science, INFORMS, vol. 51(3), pages 968-980, August.

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