Variational inequality model for cordon-based congestion pricing under side constrained stochastic user equilibrium conditions

Transportmetrica A: Transport Science

Volumn 10, Issue 8, 2014, Pages 693-704

  Liu, Zhiyuan ^a   Meng, Qiang ^b   Wang, Shuaian ^c  

^a MONASH UNIVERSITY   (Australia)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

cordon based pricing; side constraint; stochastic user equilibrium; variational inequality

Indexed keywords

MOTOR TRANSPORTATION;

CORDON-BASED CONGESTION; CORRECTION METHOD; MONOTONE PROPERTIES; ROUTE CHOICE BEHAVIOUR; SIDE CONSTRAINTS; STOCHASTIC USER EQUILIBRIUM; TRAFFIC CONDITIONS; VARIATIONAL INEQUALITIES;

VARIATIONAL TECHNIQUES;

EID: 84901349004     PISSN: 23249935     EISSN: 23249943     Source Type: Journal    
DOI: 10.1080/23249935.2013.821228     Document Type: Article

References (36)

1. Bell, M. G. H. 1995. "Alternatives to Dial's Logit Assignment Algorithm." Transportation Research Part B 29 (4): 287-295.
2. Cantarella, G. E. 1997. "A General Fixed-Point Approach to Multimode Multi-User Equilibrium Assignment with Elastic Demand." Transportation Science 31 (2): 107-128.
3. Chen, A., Z. Zhou, and S. Ryu. 2011. "Modeling Physical and Environmental Side Constraints in Traffic Equilibrium Problem." International Journal of Sustainable Transportation 5 (3): 172-197.
4. Daganzo, C. F. 1983. "Stochastic Network Equilibrium with Multiple Vehicle Types and Asymmetric, Indefinite Link Cost Jacobians." Transportation Science 17 (3): 282-300.
5. Daganzo, C. F., and Y. Sheffi. 1977. "On Stochastic Models of Traffic Assignment." Transportation Science 11 (3): 253-274.
6. Dial, R. B. 1971. "A Probabilistic Multipath Traffic Assignment Algorithm which Obviates Path Enumeration." Transportation Research 5 (2): 83-111.
7. Foo, T. S. 2000. "An Advanced Demand Management Instrument in Urban Transport: Electronic Road Pricing in Singapore." Cities 17 (1): 33-45.
8. He, B. S., and L. Z. Liao. 2002. "Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities." Journal of Optimization Theory and Applications 112 (1): 111-128.
9. Korpelevich, G. M. 1976. "The Extragradient Method for Finding Saddle Points and Other Problems." Ekonomika Matematicheskie Metody 12 (1): 747-756.
10. Larsson, T., and M. Patriksson. 1995. "An Augmented Lagrangean Dual Algorithm for Link Capacity Side Constrained Traffic Assignment Problems." Transportation Research Part B 29 (6): 433-455.
11. Larsson, T., and M. Patriksson. 1999. "Side Constrained Traffic Equilibrium Models - Analysis, Computation and Applications." Transportation Research Part B 33 (4): 233-264.
12. Lawphongpanich, S., D. W. Hearn, and M. J. Smith. 2006. Mathematical and Computational Models for Congestion Charging. New York: Springer.
13. Liu, H. X., X. He, and B. He. 2009. "Method of Successive Weighted Averages (MSWA) and Self-Regulated Averaging Schemes for Solving Stochastic User Equilibrium Problem." Networks and Spatial Economics 9 (4): 485-503.
14. Liu, Z. 2011. "Probit-based Stochastic User Equilibrium Problems and Their Applications in Congestion Pricing." PhD thesis, Department of Civil and Environmental Engineering, National University of Singapore.
15. Liu, Z., and Q. Meng. 2011. "Distributed Computing Approaches for Large-Scale Probit-based Stochastic User Equilibrium Problems." Journal of Advanced Transportation, doi:10.1002/atr.177
16. Liu, Z., and Q. Meng. 2012. "Modelling Transit-based Park-and-Ride Services on a Multimodal Network with Congestion Pricing Schemes." International Journal of Systems Science, doi:10.1080/00207721.2012.743617
17. Liu, Z., Q. Meng, and S. Wang. 2013. "Speed-based Toll Design for Cordon-based Congestion Pricing Scheme." Transportation Research Part C 31: 83-98.
18. Maher, M. J., and P. C. Hughes. 1997. "A Probit-based Stochastic User Equilibrium Assignment Model." Transportation Research Part B 31 (4): 341-355.
19. Meng, Q., W. H. K. Lam, and L. Yang. 2008. "General Stochastic User Equilibrium Traffic Assignment Problem with Link Capacity Constraints." Journal of Advanced Transportation 42 (4): 429-465.
20. Meng, Q., and Z. Liu. 2011. "Trial-and-Error Method for Congestion Pricing Scheme Under Side-Constrained Probit-based Stochastic User Equilibrium Conditions." Transportation 38 (5): 819-843.
21. Meng, Q., and Z. Liu. 2012a. "Impact Analysis of Cordon-based Congestion Pricing Scheme on Mode-Split of Bimodal Transportation Network." Transportation Research Part C 21 (1): 134-147.
22. Meng, Q., and Z. Liu. 2012b. "Mathematical Models and Computational Algorithms for Probit-based Asymmetric Stochastic User Equilibrium Problem with Elastic Demand." Transportmetrica 8 (4): 261-290.
23. Meng, Q., Z. Liu, and S. Wang. 2012. "Optimal Distance-based Toll Design for Cordon-based Congestion Pricing Scheme with Continuously Distributed Value-of-Time." Transportation Research Part E 48 (5): 937-957.
24. Meng, Q., Z. Liu, and S. Wang. 2013. "Asymmetric Stochastic User Equilibrium Problem with Link Capacity Constraints and Elastic Demand." Transportmetrica. doi:10.1080/23249935.2013.765929
25. Mun, S., K. Konishi, and K. Yoshikawa. 2003. "Optimal Cordon Pricing." Journal of Urban Economics 54 (1): 21-38.
26. Nagurney, A., and P. Ramanujam. 1998. "A Multimodal Traffic Network Equilibrium Model with Emission Pollution Permits: Compliance vs. Noncompliance." Transportation Research Part D 3 (5): 349-374.
27. Nie, Y., H. M. Zhang, and D. H. Lee. 2004. "Models and Algorithms for the Traffic Assignment Problem with Link Capacity Constraints." Transportation Research Part B 38 (4): 285-312.
28. de Palma, A., and R. Lindsey. 2011. "Traffic Congestion Pricing Methodologies and Technologies." Transportation Research Part C 19 (6): 1377-1399.
29. Pigou, A. C. 1920. The Economics of Welfare. London: MacMillan.
30. Shahpar, A. H., H. Z. Aashtiani, and A. Babazadeh. 2008. "Dynamic Penalty Function Method for the Side Constrained Traffic Assignment Problem." Applied Mathematics and Computation 206 (1): 332-345.
31. Sheffi, Y. 1985. Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Models. Englewood Cliffs, NJ: Prentice-Hall, INC.
32. Sheffi, Y., and W. B. Powell. 1982. "An Algorithm for the Equilibrium Assignment Problem with Random Link Times." Networks 12 (2): 191-207.
33. Verhoef, E. T. 2002. "Second-Best Congestion Pricing in General Networks: Heuristic Algorithms for Finding Second-Best Optimal Toll Levels and Toll Points." Transportation Research Part B 36 (8): 707-729.
34. Yan, J., K. A. Small, and E. C. Sullivan. 2002. "Choice Models of Route, Occupancy, and Time of Day with Value-Priced Tolls." Transportation Research Record 1812: 69-77.
35. Yang, H., and X. Zhang. 2002. "The Multi-Class Network Toll Design Problem with Social and Spatial Equity Constraints." Journal of Transportation Engineering, ASCE 128 (5): 420-428.
36. Zhang, X. N., and H. Yang. 2004. "The Optimal Cordon-based Network Congestion Pricing Problem." Transportation Research Part B 38 (6): 517-537.