TECHNICAL PAPERS
Oct 15, 2004

Logit-Based Stochastic User Equilibrium Problem for Entry-Exit Toll Schemes

Publication: Journal of Transportation Engineering
Volume 130, Issue 6

Abstract

This paper proposes a logit-based stochastic user equilibrium (SUE) problem for networks with entry-exit toll schemes that result in nonadditive path costs. First, it develops a strictly convex minimization model in terms of path flows for the problem. Second, by decomposing the original problem into two kinds of subproblems that possess the additive path costs, this study designs a novel two-stage stochastic loading algorithm exempted from path enumeration or generation. Hence, the method of successive average embedded with the proposed stochastic loading algorithm can identify the logit-based SUE link and entry-exit flows. Finally, two numerical examples are used to demonstrate the proposed model and algorithm.

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References

1.
Akamatsu, T. (1996). “Cyclic flows, Markov process, and stochastic traffic assignment.” Transp. Res., Part B: Methodol., 30(5), 369–386.
2.
Akamatsu, T. (1997). “Decomposition of path choices entropy in general transportation networks.” Transp. Sci., 31(4), 349–362.
3.
Bazaraa, M.S., Sherali, H.D., and Shetty, C.M. (1993). Nonlinear programming: Theory and algorithms, Wiley, New York.
4.
Bell, M. G. H. (1995). “Alternatives to Dial’s logit assignment algorithm.” Transp. Res., Part B: Methodol., 29(4), 287–295.
5.
Bell, M. G. H., and Grosso, S. (1998). “The path flow estimator as a network observer.” Traffic Eng. Control, 39(10), 540–549.
6.
Bell, M.G. H., and Iida, Y. (1997). Transportation network analysis, Wiley, New York.
8.
Ben-Akiva, M., and Bierlaire, M. (1999). “Discrete choice methods and their applications to short term travel decisions.” Handbook of transportation science, R. W. Hall, ed., Kluwer, Dordrecht, The Netherlands.
7.
Ben-Akiva, M., and Lerman, S. (1985). Discrete choice analysis: Theory and application to travel demand, MIT Press, Cambridge, Mass.
9.
Bernstein, D., and Gabriel, G. (1997). “Solving the nonadditive traffic equilibrium problem.” Network optimization, P. M. Pardalos, D. W. Hearn, and W. W. Hager, eds., Springer, New York, 72–102.
10.
Cantarella, G. E., and Binetti, M. (1998). “Stochastic equilibrium traffic assignment with value-of-time distributed among users.” Int. Trans. Oper. Res., 5(6), 541–553.
11.
Chen, A., Lo, H. K., and Yang, H. (2001). “A self-adaptive projection and contraction algorithm for the traffic assignment problem with path-specific costs.” Eur. J. Oper. Res., 135(1), 27–41.
12.
Daganzo, C. F. (1982). “Unconstrained extremal formulation of some transportation equilibrium problems.” Transp. Sci., 16(3), 332–361.
13.
Davis, G. A. (1994). “Exact local solution of the continuous network design problem via stochastic user equilibrium assignment.” Transp. Res., Part B: Methodol., 28(1), 61–75.
14.
Dial, G. A. (1971). “A probabilistic multipath traffic assignment mode which obviates the need for path enumeration.” Transp. Res., 5(1), 83–111.
15.
Fisk, C. K. (1980). “Some developments in equilibrium traffic assignment methodology.” Transp. Res., Part B: Methodol., 14(3), 243–256.
16.
Florian, M., and Hearn, D. (1995). “Network equilibrium models and algorithms.” Handbooks in operations research, Vol. 8, M. Ball et al., eds., Elsevier, New York, 485–542.
17.
Gabriel, A., and Bernstein, D. (1997). “The traffic equilibrium problem with nonadditive path costs.” Transp. Sci., 31(4), 337–349.
18.
Gabriel, A., and Bernstein, D. (2000). “Nonadditive shortest paths: Subproblems in multi-agent competitive network models.” Comput. Math.l Org. Theory, 6(1), 29–45.
19.
Huang, H.-J., and Bell, M. G. H. (1998). “A study on logit assignment which excludes all cycle flows.” Transp. Res., Part B: Methodol., 32(6), 401–412.
20.
Larsson, L., Lindberg, P.O., Lundgren, J., Patriksson, M., and Rydergren, C. (2002). “On traffic equilibrium models with a nonlinear time/money relation.” Transportation planning—State of the art, M. Patriksson and M. Labbe, eds., Kluwer, Dordrecht, The Netherlands, 19–31.
21.
Lo, H. K., and Chen, A. (1999). “Traffic equilibrium problem with route-specific costs: Formulations and algorithms.” Transp. Res., Part B: Methodol., 34(6), 493–513.
22.
Oppenheim, N. (1994). Urban travel demand modeling: From individual choice to general equilibrium, Wiley, New York.
23.
Patriksson, M. (1994). The traffic assignment problems: Models and methods, VSP, Utrecht, The Netherlands.
24.
Powell, W., and Sheffi, Y. (1982). “The convergence of equilibrium algorithm with predetermined step size.” Transp. Sci., 16(1), 45–55.
25.
Prashker, J. N., and Bekhor, S. (1998). “Investigation of stochastic network loading procedures.” Transportation Research Record 1645, Transportation Research Board, Washington, D.C., 94–102.
26.
Prashker, J. N., and Bekhor, S. (2000). “Congestion, stochastic and similarity effects in stochastic user equilibrium models.” Transportation Research Record 1733, Transportation Research Board, Washington, D.C., 80–87.
27.
Scott, K., and Bernstein, D. (1997). “Solving a best path problem when the value of time is nonlinear.” Proc., 79th Annual Meeting, Transportation Research Board, Washington, D.C.
28.
Sheffi, Y. (1985). Urban transportation networks: Equilibrium analysis with mathematical programming methods, Prentice Hall, Englewood Cliffs, N.J.
29.
Van Vliet, D. (1981). “Selected node-pair analysis in Dial’s assignment algorithm.” Transp. Res., Part B: Methodol., 15(1), 65–68.
30.
Vovsha, P., and Bekhor, S. (1998). “The link nested logit model: Overcoming the route overlapping problem.” TransportationResearch Record, Transportation Research Board, Washington, D.C., 133–142.
31.
Yang, H., and Meng, Q. (2001). “Modeling user adoption of advanced traveler information systems: Dynamic evolution and stationary equilibrium.” Transp. Res., Part A: Policy Pract., 35(10), 895–912.
32.
Yang, H., Meng, Q., and Bell, M. G. H. (2001). “Simultaneous estimation of the origin-destination matrices and travel cost coefficient for congested networks in a stochastic equilibrium.” Transp. Sci., 35(2), 107–123.
33.
Yang, H., Zhang, X., and Meng, Q. (2004). “Modeling private highways in networks with entry-exit based toll charges.” Transp. Res., Part B: Methodol. 38(3), 191–213.

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Published In

Go to Journal of Transportation Engineering
Journal of Transportation Engineering
Volume 130Issue 6November 2004
Pages: 805 - 813

History

Published online: Oct 15, 2004
Published in print: Nov 2004

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Authors

Affiliations

Qiang Meng
Assistant Professor, Dept. of Civil Engineering, National Univ. of Singapore, Singapore 117576. E-mail: [email protected]
Der-Horng Lee
Assistant Professor, Dept. of Civil Engineering, National Univ. of Singapore, Singapore 117576. E-mail: [email protected]
Ruey Long Cheu
Associate Professor, Dept. of Civil Engineering, National Univ. of Singapore, Singapore 117576. E-mail: [email protected]
Hai Yang
Professor, Dept. of Civil Engineering, Hong Kong Univ. of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. E-mail: [email protected]

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