- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 696481, 11 pages
Stochastic Congestion Pricing among Multiple Regions: Competition and Cooperation
1Centre for Maritime Studies, National University of Singapore, Singapore 118411
2School of Business, Central South University, Changsha, Hunan 410000, China
3Department of Mathematics, School of Sciences, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China
Received 17 January 2013; Accepted 3 March 2013
Academic Editor: Xiaoning Zhang
Copyright © 2013 Hua Wang 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.
- H. Yang and H. J. Huang, Mathematical and Economic Theory of Road Pricing, Elsevier, 2005.
- H. Yang and X. Zhang, “Multiclass network toll design problem with social and spatial equity constraints,” Journal of Transportation Engineering, vol. 128, no. 5, pp. 420–428, 2002.
- H. Yang and X. Zhang, “Optimal toll design in second-best link-based congestion pricing,” Transportation Research Record, no. 1857, pp. 85–92, 2003.
- H. Yang, X. Zhang, and Q. Meng, “Modeling private highways in networks with entry-exit based toll charges,” Transportation Research Part B, vol. 38, no. 3, pp. 191–213, 2004.
- X. Zhang and H. Yang, “The optimal cordon-based network congestion pricing problem,” Transportation Research Part B, vol. 38, no. 6, pp. 517–537, 2004.
- X. Zhang, H. J. Huang, and H. M. Zhang, “Integrated daily commuting patterns and optimal road tolls and parking fees in a linear city,” Transportation Research Part B, vol. 42, no. 1, pp. 38–56, 2008.
- X. Zhang, H. Yang, and H. J. Huang, “Multiclass multicriteria mixed equilibrium on networks and uniform link tolls for system optimum,” European Journal of Operational Research, vol. 189, no. 1, pp. 146–158, 2008.
- X. Zhang and B. van Wee, “Enhancing transportation network capacity by congestion pricing with simultaneous toll location and toll level optimization,” Engineering Optimization, vol. 44, no. 4, pp. 477–488, 2012.
- X. N. Zhang, H. M. Zhang, H. J. Huang, L. J. Sun, and T. Q. Tang, “Competitive, cooperative and Stackelberg congestion pricing for multiple regions in transportation networks,” Transportmetrica, vol. 7, no. 4, pp. 297–320, 2011.
- X. Zhang and B. van Wee, “Efficiency comparison of various parking charge schemes considering daily travel cost in a linear city,” European Journal of Transport and Infrastructure Research, vol. 11, no. 2, pp. 234–255, 2011.
- X. N. Zhang, H. Yang, and H. J. Huang, “Improving travel efficiency by parking permits distribution and trading,” Transportation Research Part B, vol. 45, no. 7, pp. 1018–1034, 2011.
- A. De Palma and R. Lindsey, “Private toll roads: competition under various ownership regimes,” Annals of Regional Science, vol. 34, no. 1, pp. 13–35, 2000.
- B. Ubbels and E. T. Verhoef, “Governmental competition in road charging and capacity choice,” Regional Science and Urban Economics, vol. 38, no. 2, pp. 174–190, 2008.
- A. Yuen, L. J. Basso, and A. Zhang, “Effects of gateway congestion pricing on optimal road pricing and hinterland,” Journal of Transport Economics and Policy, vol. 42, no. 3, pp. 495–526, 2008.
- A. Sumalee and W. Xu, “First-best marginal cost toll for a traffic network with stochastic demand,” Transportation Research Part B, vol. 45, no. 1, pp. 41–59, 2011.
- A. C. Pigou, The Economics of Welfare, MacMillan, London, UK, 1920.
- F. H. Knight, “Some fallacies in the interpretation of social costs,” Quarterly Journal of Economics, vol. 38, pp. 582–606, 1924.
- H. Yang and H. J. Huang, “Principle of marginal-cost pricing: how does it work in a general road network?” Transportation Research Part A, vol. 32, no. 1, pp. 45–54, 1998.
- H. Yang, “System optimum, stochastic user equilibrium, and optimal link tolls,” Transportation Science, vol. 33, no. 4, pp. 354–360, 1999.
- S. T. Waller and A. K. Ziliaskopoulos, “Stochastic dynamic network design problem,” Transportation Research Record, no. 1771, pp. 106–113, 2001.
- G. R. Patil and S. V. Ukkusuri, “System-optimal stochastic transportation network design,” Transportation Research Record, no. 2029, pp. 80–86, 2007.
- A. Chen, Z. Ji, and W. Recker, “Travel time reliability with risk-sensitive travelers,” Transportation Research Record, no. 1783, pp. 27–33, 2002.
- S. Nakayama and J. Takayama, “A traffic network equilibrium model for uncertain demands,” in Proceedings of the 82nd Transportation Research Board Annual Meeting, 2003.
- S. Clark and D. Watling, “Modelling network travel time reliability under stochastic demand,” Transportation Research Part B, vol. 39, no. 2, pp. 119–140, 2005.
- H. Shao, W. H. K. Lam, Q. Meng, and M. L. Tam, “Demand-driven traffic assignment problem based on travel time reliability,” Transportation Research Record, no. 1985, pp. 220–230, 2006.
- H. Shao, W. H. K. Lam, and M. L. Tam, “A reliability-based stochastic traffic assignment model for network with multiple user classes under uncertainty in demand,” Networks and Spatial Economics, vol. 6, no. 3-4, pp. 173–204, 2006.
- W. H. K. Lam, H. Shao, and A. Sumalee, “Modeling impacts of adverse weather conditions on a road network with uncertainties in demand and supply,” Transportation Research Part B, vol. 42, no. 10, pp. 890–910, 2008.
- B. Y. Chen, W. H. K. Lam, A. Sumalee, and H. Shao, “An efficient solution algorithm for solving multi-class reliability-based traffic assignment problem,” Mathematical and Computer Modelling, vol. 54, no. 5-6, pp. 1428–1439, 2011.
- H. Li, M. C. J. Bliemer, and P. H. L. Bovy, “Network reliability-based optimal toll design,” Journal of Advanced Transportation, vol. 42, no. 3, pp. 311–332, 2008.
- S. D. Boyles, K. M. Kockelman, and S. T. Waller, “Congestion pricing under operational, supply-side uncertainty,” Transportation Research Part C, vol. 18, no. 4, pp. 519–535, 2010.
- L. M. Gardner, S. D. Boyles, and S. T. Waller, “Quantifying the benefit of responsive pricing and travel information in the stochastic congestion pricing problem,” Transportation Research Part A, vol. 45, no. 3, pp. 202–218, 2011.
- R. W. Hall, “Travel outcome and performance: the effect of uncertainty on accessibility,” Transportation Research Part B, vol. 17, no. 4, pp. 275–290, 1983.
- Y. Sheffi, Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods, Prentice Hall, Englewood Cliff, NJ, USA, 1985.
- J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM Journal on Optimization, vol. 9, no. 1, pp. 112–147, 1999.
- V. Torczon, “On the convergence of pattern search algorithms,” SIAM Journal on Optimization, vol. 7, no. 1, pp. 1–25, 1997.
- C. Audet and J. E. Dennis, “Analysis of generalized pattern searches,” SIAM Journal on Optimization, vol. 13, no. 3, pp. 889–903, 2003.