A Dual Variable Approximation Based Heuristic for Dynamic Congestion Pricing

Networks and Spatial Economics

Volumn 11, Issue 2, 2011, Pages 271-293

  Lin, Dung Ying ^a   Unnikrishnan, Avinash ^b   Waller, Travis ^c  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^b West Virginia University   (United States)

^c The University of Texas at Austin   (United States)

Author keywords

Dual variable approximation; Dynamic congestion pricing; Method of successive average

Indexed keywords

EID: 79955468238     PISSN: 1566113X     EISSN: 15729427     Source Type: Journal    
DOI: 10.1007/s11067-009-9124-9     Document Type: Article

References (54)

1. Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms and applications. Prentice Hall, New Jersey.
2. Arnott R, de Palma A, Lindsey R (1990) Economics of a bottleneck. J Urban Econ 27: 11-30.
3. Arnott R, Small K (1994) The economics of traffic congestion. Am Sci 20(2): 123-127.
4. Arnott R, Kraus M (1998) When are anonymous congestion charges consistent with marginal cost pricing. J Public Econ 67: 45-64.
5. Braid RM (1996) Peak-load pricing of a transport facility with an unpriced substitute. J Urban Econ 40: 179-197.
6. Bureau of Public Roads (1964) Traffic assignment manual. U. S. Dept. of Commerce, Urban Planning Division, Washington D. C.
7. Carey M, Srinivasan A (1993) Externalities, average and marginal costs, and tolls on congested networks with timevarying flows. Oper Res 41(1): 217-231.
8. Chang EJ (2004) Time-varying intermodal person trip assignment. Ph. D. Dissertation, Northwestern University.
9. Chiou SW (2005) Bilevel programming for the continuous transport network design problem. Transp Res Part B 39(4): 361-383.
10. Chiou S-W (2006) An optimal scheme for toll pricing problem. Appl Math Comput 80(2): 1127-1136.
11. Chu X (1995) Endogenous trip scheduling: the Henderson approach reformulated and compared with the Vickrey approach. J Urban Econ 37: 324-343.
12. Daganzo CF (1994) The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transp Res Part B 28B(4): 269-287.
13. Daganzo CF (1995) The cell transmission model, part II: network traffic. Transp Res Part B 29B(2): 79-93.
14. De Palma A, Lindsey R (2000) Private toll roads: competition under various ownership regimes. Ann Reg Sci 34(1): 13-35.
15. De Palma A, Kilani M, Lindsey R (2005) Congestion pricing on a road network: a study using the dynamic equilibrium simulator METROPOLIS. Transp Res Part A 39: 588-611.
16. Duthie J, Waller ST (2008) Incorporating environmental justice measures into equilibrium-based network design. Transp Res Rec: J Transp Res Board 2089: 58-65.
17. Ferrari P (2002) Road network toll pricing and social welfare. Transp Res, Part B 36(5): 471-483.
18. Friesz TL, Cho HJ, Mehta NJ, Tobin RL, Anandalingam G (1992) A simulated annealing approach to the network design problem with variational inequality constraints. Transp Sci 26(1): 18-26.
19. Gardner LM, Unnikrishnan A, Waller ST (2008) Robust pricing of transportation networks under uncertain demand. Transp Res Rec: J Transp Res Board 2085: 21-30.
20. Gedeon C, Florian M, Crainic TG (1993) Determining origin-destination matrices and optimal multiproduct flows for freight transportation over multimodal networks. Transp Res Part B 27: 351-368.
21. Hearn DW, Yildirim MB (2001) A toll pricing framework for traffic assignment problems with elastic demands. In: Miscellanea in Honor of Michael Florian, Gendreau M, Marcotte P (eds) Current trends in transportation and network analysis. Kluwer, Dordrecht.
22. Henderson JV (1974) Road congestion: a reconsideration of pricing theory. J Urban Econ 1: 346-365.
23. Henderson JV (1981) The economics of staggered work hours. J Urban Econ 9: 349-364.
24. Joksimovic D, Bliemer MCJ, Bovy PHL (2005) Optimal toll design problem in dynamic traffic networks with joint route and departure time choice. J Transp Res Board 1923: 61-72.
25. Josefsson M, Patriksson M (2007) Sensitivity analysis of separable traffic equilibrium equilibria with application to bilevel optimization in network design. Transp Res Part B 41: 4-31.
26. Karoonsoontawong A, Waller ST (2005) Comparison of system and user optimal stochastic dynamic network design models using Monte Carlo bounding techniques. Transp Res Rec: J Transp Res Board 1923: 91-102.
27. Knight FH (1924) Some fallacies in the interpretation of social cost. Q J Econ 38: 582-606.
28. Labbe M, Marcotte P, Savard G (1998) A bilevel model of taxation and its application to optimal highway pricing. Manag Sci 44(12): 1608-1622.
29. Lawphongpanich S, Hearn DW (2004) An MPEC approach to second best toll pricing. Math Program, Series B 101(1): 33-55.
30. Leblanc LJ, Boyce DE (1986) A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows. Transp Res Part B 20(3): 259-265.
31. Li Y, Waller ST, Ziliaskopoulos T (2003) A decomposition scheme for system optimal dynamic traffic assignment models. Trans Res Rec 3(4): 441-455.
32. Lighthill MJ, Whitham JB (1955) On kinematic waves II: a theory of traffic flow on long crowded roads. Proc R Soc Lond, A Math Phys Sci 229(1178): 317-345.
33. Lim AC (2002) Transportation network design problem: an MPEC approach. PhD thesis, Johns Hopkins University.
34. Lin D-Y, Karoonsoontawong A, Waller ST (2009a) A Dantzig-Wolfe decomposition based heuristic scheme for bi-level dynamic network design problem. Networks and Spatial Economics, http://dx. doi. org/10. 1007/s11067-008-9093-4.
35. Lin D-Y, Unnikrishnan A, Waller ST (2009b) A genetic algorithm for bi-level linear programming dynamic network design problem. Transportation Letters: The International Journal of Transportation Research 1(4): 281-294.
36. Luo ZQ, Pang JS, Ralph D (1996) Mathematical programs with equilibrium constraints, Cambridge University Press.
37. Morrison SA (1986) A survey of road pricing. Transp Res 20A(2): 87-97.
38. Oregon Department of Transportation: Policy and Economic Analysis Unit (2003) The value-of-travel time: estimates of the hourly value of time for vehicles in Oregon 2003.
39. Patriksson M, Rockafellar RT (2002) A mathematical model and descent algorithm for bilevel traffic management. Transp Sci 36(3): 271-291.
40. Pigou AC (1920) The economics of welfare. Macmillan and Co., London.
41. Richards PI (1956) Shockwaves on the highway. Oper Res 4: 42-51.
42. Tobin RL, Friesz TL (1988) Sensitivity analysis for equilibrium network flow. Transp Sci 22: 242-250.
43. Ukkusuri S (2002) Linear programs for the user optimal dynamic traffic assignment problem. Master Thesis, University of Illinois at Urbana-Champaign.
44. Ukkusuri S, Waller ST (2008) Linear programming models for the user and system optimal dynamic network design problem: formulations, comparisons and extensions. Networks and Spatial Economics 8(4): 383-406.
45. Verhoef ET (2002) Second-best congestion pricing in general networks: algorithms for finding second-best optimal toll levels and toll points. Transp Res Part B 36(8): 707-729.
46. Vickrey WS (1969) Congestion theory and transport investment. Am Econ Rev 59: 251-260, Papers and Proceedings.
47. Waller ST (2000) Optimization and control of stochastic dynamic transportation systems: formulations, solution methodologies, and computational experience. Ph. D. Dissertation, Northwestern University.
48. Walters AA (1961) The theory and measurement of private and social cost of highway congestion. Econometrica 29: 676-699.
49. Wie B-W (2007) Dynamic Stackelberg equilibrium congestion pricing. Transp Res Part C 15: 154-174.
50. Wie B, Tobin RL (1998) Dynamic congestion pricing models for general traffic networks. Transportation Record Part B 32(5): 313-327.
51. Yang H, Lam WHK (1996) Optimal road tolls under conditions of queuing and congestion. Transp Res Part A 30(5): 319-332.
52. Yang H, Huang H-J (1997) Analysis of time-varying pricing of a bottleneck with elastic demand using optimal control theory. Transp Res Part B 31B(6): 425-440.
53. Yildirim MB, Hearn DW (2005) A first best toll pricing/next term framework for variable demand traffic assignment problems. Transp Res Part B 39: 659-678.
54. Ziliaskopoulos AK (2000) A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transp Sci 34(1): 37-49.