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On the local and global stability of a travel route choice adjustment process

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  • Zhang, Ding
  • Nagurney, Anna

Abstract

This paper presents a stability analysis for the dynamic model of a travel route choice adjustment process proposed by Dupuis and Nagurney (1993). In particular, we investigate both local and global stability issues for this adjustment process that may be of concern to transportation planners and analysts. Two distinct approaches for stability analysis are proposed based on the general stability analysis results obtained recently by Zhang and Nagurney (1995) for projected dynamical systems. The global stability results are established using a "monotonicity" approach, under monotonicity assumptions on the link cost and travel disutility functions. A distinct approach, termed a "regularity" approach, is then provided to verify the local stability of the adjustment process at a regular equilibrium flow pattern.

Suggested Citation

  • Zhang, Ding & Nagurney, Anna, 1996. "On the local and global stability of a travel route choice adjustment process," Transportation Research Part B: Methodological, Elsevier, vol. 30(4), pages 245-262, August.
  • Handle: RePEc:eee:transb:v:30:y:1996:i:4:p:245-262
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    References listed on IDEAS

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    1. Dafermos, Stella & Nagurney, Anna, 1984. "On some traffic equilibrium theory paradoxes," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 101-110, April.
    2. 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.
    3. 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.
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    Cited by:

    1. Huang, Hai-Jun & Lam, William H. K., 2002. "Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 253-273, March.
    2. 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.
    3. Ye, Hongbo & Yang, Hai, 2013. "Continuous price and flow dynamics of tradable mobility credits," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 436-450.
    4. repec:eee:transb:v:104:y:2017:i:c:p:1-16 is not listed on IDEAS
    5. Iryo, Takamasa, 2016. "Day-to-day dynamical model incorporating an explicit description of individuals’ information collection behaviour," Transportation Research Part B: Methodological, Elsevier, vol. 92(PA), pages 88-103.
    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. 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.
    9. Nagurney, Anna & Zhang, Ding, 1998. "A massively parallel implementation of a discrete-time algorithm for the computation of dynamic elastic demand traffic problems modeled as projected dynamical systems," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1467-1485, August.
    10. Wang, Jian & He, Xiaozheng & Peeta, Srinivas, 2016. "Sensitivity analysis based approximation models for day-to-day link flow evolution process," Transportation Research Part B: Methodological, Elsevier, vol. 92(PA), pages 35-53.
    11. He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2010. "A link-based day-to-day traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 597-608, May.
    12. Farokhi, Farhad & Johansson, Karl H., 2015. "A piecewise-constant congestion taxing policy for repeated routing games," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 123-143.
    13. 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.
    14. 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.
    15. Watling, David, 1999. "Stability of the stochastic equilibrium assignment problem: a dynamical systems approach," Transportation Research Part B: Methodological, Elsevier, vol. 33(4), pages 281-312, May.
    16. 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.
    17. Ye, Hongbo & Yang, Hai & Tan, Zhijia, 2015. "Learning marginal-cost pricing via a trial-and-error procedure with day-to-day flow dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 794-807.
    18. Bie, Jing & Lo, Hong K., 2010. "Stability and attraction domains of traffic equilibria in a day-to-day dynamical system formulation," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 90-107, January.

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