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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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    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. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    3. 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.
    4. Michael J. Smith, 1984. "The Stability of a Dynamic Model of Traffic Assignment---An Application of a Method of Lyapunov," Transportation Science, INFORMS, vol. 18(3), pages 245-252, August.
    5. 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.
    6. Marguerite Frank, 1989. "The Equilibrium Worth of a Network Link," Transportation Science, INFORMS, vol. 23(2), pages 125-138, May.
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