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Bayesian Learning, Day-to-day Adjustment Process, and Stability of Wardrop Equilibrium

  • Shoichiro Nakayama
Chapter

Abstract

In this study, we assume that drivers under day-to-day dynamic transportation circumstances choose routes based on Bayesian learning and develop a day-to-day dynamic model of network flow. This model reveals that a driver using Bayesian learning chooses the route that frequently takes the minimum travel time. Furthermore, we find that the equilibrium point of the day-to-day dynamic model is identical to Wardrop’s equilibrium. Under complete information (when information about which route takes the minimum travel time is given after the trips), Wardrop’s equilibrium is globally asymptotically stable and the day-to-day dynamic system converges to Wardrop’s equilibrium if initial recognition among drivers is distributed widely. Under incomplete information, Wardrop’s equilibrium is always globally asymptotically stable regardless of what the drivers’ initial recognition is. Paradoxically, the condition for stable equilibrium under incomplete information is more relaxed than that under complete information.

Keywords

Travel Time Subjective Probability Rational Expectation Route Choice Network Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Beckmann, M., McGuire, C.G. and Winsten, C.B. (1956). Studies in Economics of Transportation. New Haven: Yale University Press.Google Scholar
  2. Canterella, G.E. and Cascetta, E. (1995). Dynamic process and equilibrium in transportation networks: towards a unifying theory. Transportation Science, 29(4), 305-329.CrossRefGoogle Scholar
  3. Daganzo, C.F. and Sheffi, Y. (1977). On stochastic models of traffic assignment. Transportation Science, 11, 253-274.CrossRefGoogle Scholar
  4. Dupuis, P. and Nagurney, A. (1993). Dynamical systems and variational inequalities. Annals of Operations Research, 44, 9-42.Google Scholar
  5. Elaydi, S.N. (1999). An Introduction to Difference Equations, 2nd Ed., New York: Springer.Google Scholar
  6. Emmerink, R.H.M., Axhausen, K.W., Nijkamp, P. and Rietveld, P. (1995). Effects of information in road transport networks with recurrent congestion. Transportation, 22, 21-53.CrossRefGoogle Scholar
  7. Friesz, T.L., Bernstein, D., Mehta, N.J., Tobin, R.L. and Ganjalizadeh, S. (1994). Day-to-day dynamic network disequilibria and idealized traveler information systems. Operations Research, 42(6), 1120-1136.CrossRefGoogle Scholar
  8. Horowitz, J.L. (1984). The stability of stochastic equilibrium in a two-link transportation network. Transportation Research Part B, 18, 13-28.CrossRefGoogle Scholar
  9. Jha, M., Madanat, S., and Peeta, S. (1998). Perception updating and day-to-day travel choice dynamics in traffic networks with information provision. Transportation Research Part C, 6, 189-212.CrossRefGoogle Scholar
  10. Kobayashi, K. (1994) Information, rational expectations, and network equilibria—an analytical perspective for route guidance systems. The Annals of Regional Science, 28, 369-393.CrossRefGoogle Scholar
  11. Kobayashi, K. and Tatano, H. (1996). Traffic network equilibria with rational expectations. Interdisciplinary Information Sciences, 2, 189-198.CrossRefGoogle Scholar
  12. Muth, J.F. (1961). Rational expectations and the theory of price movements. Econometrica, 29, 315-335.CrossRefGoogle Scholar
  13. Nagurney, A. and Zhang, D. (1997). Projected dynamical systems in the formulation, stability analysis, and computation of fixed-demand traffic network equilibrium. Transportation Science, 31(2), 147-158.CrossRefGoogle Scholar
  14. Nakayama, S., Kitamura, R.and Fujii, S. (1999). Drivers’ learning and network behavior: a dynamic analysis of the driver-network system as a complex system. Transportation Research Record, 1676, 30-36.CrossRefGoogle Scholar
  15. Sheffrin, S.M. (1996). Rational Expectations. 2nd Ed., Cambridge, Cambridge University Press.Google Scholar
  16. Smith, M.J. (1984). The stability of a dynamic model of traffic assignment: an application of a method of Lyapunov. Transportation Science, 18(3), 245-252.CrossRefGoogle Scholar
  17. Wardrop, J.G. (1952). Some theoretical aspects of road traffic research. Proceedings of the Institution of Civil Engineers, Part II, 1, 325-378.Google Scholar
  18. Watling, D. (1999). Stability of the stochastic equilibrium assignment problem: A dynamical systems approach. Transportation Research Part B, 33, 281-312.CrossRefGoogle Scholar
  19. Zangwill, W.I. (1969). Nonlinear Programming: A Unified Approach. Englewood Cliffs, N.J., Prentice-Hall.Google Scholar
  20. Zhang, D. and Nagurney, A. (1996). On the local and global stability of a travel route choice adjustment process. Transportation Research Part B, 30, 245-262.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  • Shoichiro Nakayama
    • 1
  1. 1.Kanazawa University, Japan and University of LeedsLondonU.K

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