Copyright © 2012 Bingfeng Si 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.

Linked References

1. Beijing Transportation Research Center (BTRC), “Investigation and analysis of Beijing residents' travel behavior in 2010,” Research Report, Beijing, China, 2011.
2. A. B. Beckmann, C. B. McGuire, and C. B. Winsten, Studies in the Economics of Transportation, Yale University Press, New Haven, Conn, USA, 1956.
3. Y. Sheffi, Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods, Prentice-Hall, Englewood Cliffs, NJ, USA, 1985.
4. M. Patriksson, The Traffic Assignment Problem: Models and Methods, VSP, Utrecht, The Netherlands, 1994.
5. M. Florian, “A traffic equilibrium model of travel by car and public transit modes,” Transportation Science, vol. 11, no. 2, pp. 166–179, 1977. View at Publisher · View at Google Scholar · View at Scopus
6. M. Florian and H. Spiess, “On binary mode choice/assignment models,” Transportation Science, vol. 17, no. 1, pp. 32–47, 1983. View at Publisher · View at Google Scholar · View at Scopus
7. A. B. Nagurney, “Comparative tests of multimodal traffic equilibrium methods,” Transportation Research Part B, vol. 18, no. 6, pp. 469–485, 1984. View at Publisher · View at Google Scholar · View at Scopus
8. S. C. Wong, “Multi-commodity traffic assignment by continuum approximation of network flow with variable demand,” Transportation Research Part B, vol. 32B, no. 8, pp. 567–581, 1998. View at Scopus
9. P. Ferrari, “A model of urban transport management,” Transportation Research Part B, vol. 33B, no. 1, pp. 43–61, 1999. View at Scopus
10. S. Li, W. Deng, and Y. Lv, “Combined modal split and assignment model for the multimodal transportation network of the economic circle in China,” Transport, vol. 24, no. 3, pp. 241–248, 2009. View at Publisher · View at Google Scholar · View at Scopus
11. M. Florian and S. Nguyen, “A combined trip distribution modal split and trip assignment model,” Transportation Research, vol. 12, no. 4, pp. 241–246, 1978. View at Publisher · View at Google Scholar · View at Scopus
12. K. N. A. Safwat and T. L. Magnanti, “A combined trip generation, trip distribution, modal split, and trip assignment model,” Transportation Science, vol. 22, no. 1, pp. 14–30, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
13. T. Abrahamsson and L. Lundqvist, “Formulation and estimation of combined network equilibrium models with applications to Stockholm,” Transportation Science, vol. 33, no. 1, pp. 80–100, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
14. D. Boyce, “Network equilibrium models of urban location and travel choices: a new research agenda,” in New Frontiers in Regional Science, M. Chatterji and R. E. Kuenne, Eds., pp. 238–256, Macmillan, New York, NY, USA, 1990.
15. D. Boyce, “Long-term advances in the state of the art of travel forecasting methods,” in Equilibrium and Advanced Transportation ModelingEdited By, P. Marcotte and S. Nguyen, Eds., pp. 73–86, Kluwer, Dordrecht, The Nertherlands, 1998. View at Zentralblatt MATH
16. C. S. Fisk and D. E. Boyce, “Alternative variationa1 inequality formulations of the network equilibrium travel choice problem,” Transportation Science, vol. 17, no. 4, pp. 454–463, 1983. View at Publisher · View at Google Scholar · View at Scopus
17. M. Florian, J. H. Wu, and S. He, “A multi-class multi-mode variable demand network equilibrium model with hierarchical logit structures,” in Transportation and Network Analysis: Current Trends, vol. 63, pp. 119–133, Kluwer Academic Publishers, London, UK, 2002. View at Zentralblatt MATH
18. B. Si, J. Long, and Z. Gao, “Optimization model and algorithm for mixed traffic of urban road network with flow interference,” Science in China. Series E, vol. 51, no. 12, pp. 2223–2232, 2008. View at Publisher · View at Google Scholar
19. B. F. Si, M. Zhong, and Z. Y. Gao, “A link resistance function of urban mixed traffic network,” Journal of Transportation Systems Engineering and Information Technology, vol. 8, no. 1, pp. 68–73, 2008. View at Scopus
20. Z. Zhou, A. Chen, and S. C. Wong, “Alternative formulations of a combined trip generation, trip distribution, modal split, and trip assignment model,” European Journal of Operational Research, vol. 198, no. 1, pp. 129–138, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
21. M. Xu and Z. Y. Gao, “Multi-class multi-modal network equilibrium with regular choice behaviors: a general fixed point approach,” in Transportation and Traffic Theory, W. H. K. Lam, S. C. Wong, and H. K. Lo, Eds., pp. 301–325, Springer, 2009.
22. A. Nagurney, “A multiclass, multicriteria traffic network equilibrium model,” Mathematical and Computer Modelling, vol. 32, no. 3-4, pp. 393–411, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
23. R. B. Dial, “A model and algorithm for multicriteria route-mode choice,” Transportation Research Part B, vol. 13, no. 4, pp. 311–316, 1979. View at Publisher · View at Google Scholar · View at Scopus
24. S. Dafermos, A Multicriteria Route-Mode Choice Traffic Equilibrium Model, Lefschetz Center for Dynamical Systems, Brown University, Providence, RI, USA, 1981.
25. A. Nagurney and J. Dong, “A multiclass, multicriteria traffic network equilibrium model with elastic demand,” Transportation Research Part B, vol. 36, no. 5, pp. 445–469, 2002. View at Publisher · View at Google Scholar · View at Scopus
26. M. C. J. Bliemer and P. H. L. Bovy, “Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem,” Transportation Research Part B, vol. 37, no. 6, pp. 501–519, 2003. View at Publisher · View at Google Scholar · View at Scopus
27. K. I. Wong, S. C. Wong, J. H. Wu, H. Yang, and W. H. K. Lam, “A combined distribution, hierarchical mode choice, and assignment network model with multiple user and mode classes,” in Urban and Regional Transportation Modeling, Essays in Honor of David Boyce, pp. 25–42, 2004.
28. M. Mainguenaud, “Modelling the network component of geographical information systems,” International Journal of Geographical Information Systems, vol. 9, no. 6, pp. 575–593, 1995. View at Publisher · View at Google Scholar · View at Scopus
29. N. Jing, Y. W. Huang, and E. A. Rundensteiner, “Hierarchical encoded path views for path query processing: an optimal model and its performance evaluation,” IEEE Transactions on Knowledge and Data Engineering, vol. 10, no. 3, pp. 409–432, 1998. View at Publisher · View at Google Scholar · View at Scopus
30. R. Van Nes, “Hierarchical levels networks in the design of multimodal transport networks,” in Proceedings of the Nectar Conference, Delft, The Netherlands, 1999. View at Publisher · View at Google Scholar
31. S. Jung and S. Pramanik, “An efficient path computation model for hierarchically structured topographical road maps,” IEEE Transactions on Knowledge and Data Engineering, vol. 14, no. 5, pp. 1029–1046, 2002. View at Publisher · View at Google Scholar · View at Scopus
32. H. K. Lo, C. W. Yip, and K. H. Wan, “Modeling transfer and non-linear fare structure in multi-modal network,” Transportation Research B, vol. 37, pp. 149–170, 2003. View at Publisher · View at Google Scholar
33. Z. X. Wu and W. H. K. Lam, “Network equilibrium for congested multi-mode networks with elastic demand,” Journal of Advanced Transportation, vol. 37, no. 3, pp. 295–318, 2003. View at Publisher · View at Google Scholar · View at Scopus
34. R. García and A. Marín, “Network equilibrium with combined modes: models and solution algorithms,” Transportation Research Part B, vol. 39, no. 3, pp. 223–254, 2005. View at Publisher · View at Google Scholar · View at Scopus
35. B. Si, M. Zhong, and Z. Gao, “Bilevel programming for evaluating revenue strategy of railway passenger transport under multimodal market competition,” Transportation Research Record, no. 2117, pp. 1–6, 2009. View at Publisher · View at Google Scholar · View at Scopus
36. B. Si, M. Zhong, H. Sun, and Z. Gao, “Equilibrium model and algorithm of urban transit assignment based on augmented network,” Science in China. Series E, vol. 52, no. 11, pp. 3158–3167, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
37. B. Si, M. Zhong, X. Yang, and Z. Gao, “Urban transit assignment model based on augmented network with in-vehicle congestion and transfer congestion,” Journal of Systems Science and Systems Engineering, vol. 20, no. 2, pp. 155–172, 2011. View at Publisher · View at Google Scholar · View at Scopus
38. A. Nagurney, Network Economics: A Variational Inequality Approach, vol. 1 of Advances in Computational Economics, Kluwer Academic Publishers, Dordrecht, The Netherrlands, 1993. View at Publisher · View at Google Scholar
39. L. J. LeBlanc and D. E. Boyce, “A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows,” Transportation Research B, vol. 20, no. 3, pp. 259–265, 1986. View at Publisher · View at Google Scholar
40. C. Suwansirikul, T. L. Friesz, and R. L. Tobin, “Equilibrium decomposed optimization: a heuristic for the continuous equilibrium network design problem,” Transportation Science, vol. 21, no. 4, pp. 254–263, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
41. J. Clegg, M. Smith, Y. Xiang, and R. Yarrow, “Bilevel programming applied to optimising urban transportation,” Transportation Research Part B, vol. 35, no. 1, pp. 41–70, 2001. View at Publisher · View at Google Scholar · View at Scopus
42. M. Patriksson, “On the applicability and solution of bilevel optimization models in transportation science: a study on the existence, stability and computation of optimal solutions to stochastic mathematical programs with equilibrium constraints,” Transportation Research Part B, vol. 42, no. 10, pp. 843–860, 2008. View at Publisher · View at Google Scholar · View at Scopus
43. R. L. Tobin and T. L. Friesz, “Sensitivity analysis for equilibrium network flow,” Transportation Science, vol. 22, no. 4, pp. 242–250, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
44. P. T. Harker, “Accelerating the convergence of the diagonalization and projection algorithms for finite-dimensional variational inequalities,” Mathematical Programming, vol. 41, no. 1, pp. 29–59, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
45. D. Boyce, B. Ralevic-Dekic, and H. Bar-Gera, “Convergence of traffic assignments: how much is enough?” Journal of Transportation Engineering, vol. 130, no. 1, pp. 49–55, 2004. View at Publisher · View at Google Scholar · View at Scopus