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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 162128, 10 pages
Nonlinear Min-Cost-Pursued Route-Swapping Dynamic System
MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology,
Beijing Jiaotong University, Beijing 100044, China
Received 29 January 2013; Accepted 23 April 2013
Academic Editor: Leonid Shaikhet
Copyright © 2013 Wenyi Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. J. Smith, “The stability of a dynamic model of traffic assignment—an application of a method of Lyapunov,” Transportation Science, vol. 18, no. 3, pp. 245–252, 1984.
- R. Mounce and M. Carey, “Route swapping in dynamic traffic networks,” Transportation Research B, vol. 45, no. 1, pp. 102–111, 2011.
- H. J. Cho and M. C. Hwang, “A stimulus-response model of day-to-day network dynamics,” IEEE Transactions on Intelligent Transportation Systems, vol. 6, no. 1, pp. 17–25, 2005.
- H.-J. Cho and M.-C. Hwang, “Day-to-day vehicular flow dynamics in intelligent transportation network,” Mathematical and Computer Modelling, vol. 41, no. 4-5, pp. 501–522, 2005.
- M. J. Smith and M. B. Wisten, “A continuous day-to-day traffic assignment model and the existence of a continuous dynamic user equilibrium,” Annals of Operations Research, vol. 60, no. 1, pp. 59–79, 1995.
- H. J. Huang and W. H. K. Lam, “Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues,” Transportation Research B, vol. 36, no. 3, pp. 253–273, 2002.
- S. Peeta and T.-H. Yang, “Stability issues for dynamic traffic assignment,” Automatica, vol. 39, no. 1, pp. 21–34, 2003.
- M. J. Smith and R. Mounce, “A splitting rate model of traffic re-routing and traffic control,” Transportation Research B, vol. 45, no. 9, pp. 1389–1409, 2011.
- W. Y. Zhang, W. Guan, J. H. Ma, and J. F. Tian, “A nonlinear pair-wise swapping dynamic to model the selfish rerouting evolutionary game,” http://eprintweb.org/S/article/math/1305.5046.
- Z. Zhou and A. Chen, “Comparative analysis of three user equilibrium models under stochastic demand,” Journal of Advanced Transportation, vol. 42, no. 3, pp. 239–263, 2008.
- D. P. Walting and M. Hazelton, “The dynamics and equilibria of day-to-day assignment models,” Networks and Spatial Economics, vol. 3, pp. 349–370, 2003.
- J. G. Wardrop, “Some theoretical aspects of road traffic research,” in Proceedings of the Institution of Civil Engineers, Part II: Research and Theory, pp. 325–378, 1952.
- F. Yang and D. Zhang, “Day-to-day stationary link flow pattern,” Transportation Research B, vol. 43, no. 1, pp. 119–126, 2009.
- D. Zhang, A. Nagurney, and J. Wu, “On the equivalence between stationary link flow patterns and traffic network equilibria,” Transportation Research B, vol. 35, no. 8, pp. 731–748, 2001.
- H. K. Khalil, Nonlinear Systems, Prentice-Hall, Upper Saddle River, NJ, USA, 3rd edition, 2002.