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Bicriterion traffic assignment: Efficient algorithms plus examples

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  • Dial, Robert B.

Abstract

This paper describes the mathematical properties and solution algorithm of a stochastic bicriterion equilibrium traffic assignment model in which both criteria may be flow-dependent. Formulated as a variational inequality, the model can reflect that different trip makers--due to habit, taste, or information--react differently to various factors such as travel time, out-of-pocket cost, and traffic congestion. Combining a novel tree builder/trip loader that obviates path enumeration together with Newton's method and linear programming, its reduced simplicial decomposition solution algorithm is fast enough to make the model a practical planning tool.

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  • Dial, Robert B., 1997. "Bicriterion traffic assignment: Efficient algorithms plus examples," Transportation Research Part B: Methodological, Elsevier, vol. 31(5), pages 357-379, October.
    • Handle: RePEc:eee:transb:v:31:y:1997:i:5:p:357-379
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    References listed on IDEAS

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    1. Dial, Robert B., 1979. "A model and algorithm for multicriteria route-mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 311-316, December.
    2. Robert B. Dial, 1996. "Bicriterion Traffic Assignment: Basic Theory and Elementary Algorithms," Transportation Science, INFORMS, vol. 30(2), pages 93-111, May.
    3. Terry L. Friesz & David Bernstein & Tony E. Smith & Roger L. Tobin & B. W. Wie, 1993. "A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem," Operations Research, INFORMS, vol. 41(1), pages 179-191, February.
    4. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    5. Lawphongpanich, Siriphong & Hearn, Donald W., 1984. "Simplical decomposition of the asymmetric traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 123-133, April.
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    3. Xu, Zhandong & Chen, Anthony & Liu, Xiaobo, 2023. "Time and toll trade-off with heterogeneous users: A continuous time surplus maximization bi-objective user equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 31-58.
    4. Hong, Sung-Pil & Kim, Kyung min & Byeon, Geunyeong & Min, Yun-Hong, 2017. "A method to directly derive taste heterogeneity of travellers’ route choice in public transport from observed routes," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 41-52.
    5. Danczyk, Adam & Di, Xuan & Liu, Henry X. & Levinson, David M., 2017. "Unexpected versus expected network disruption: Effects on travel behavior," Transport Policy, Elsevier, vol. 57(C), pages 68-78.
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    7. Wang, Judith Y.T. & Ehrgott, Matthias, 2013. "Modelling route choice behaviour in a tolled road network with a time surplus maximisation bi-objective user equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 342-360.
    8. Zhang, Xiaoning & Yang, Hai & Huang, Hai-Jun, 2008. "Multiclass multicriteria mixed equilibrium on networks and uniform link tolls for system optimum," European Journal of Operational Research, Elsevier, vol. 189(1), pages 146-158, August.
    9. Wang, Guangchao & Jia, Ning & Ma, Shoufeng & Qi, Hang, 2014. "A rank-dependent bi-criterion equilibrium model for stochastic transportation environment," European Journal of Operational Research, Elsevier, vol. 235(3), pages 511-529.
    10. Siu, Barbara W.Y. & Lo, Hong K., 2008. "Doubly uncertain transportation network: Degradable capacity and stochastic demand," European Journal of Operational Research, Elsevier, vol. 191(1), pages 166-181, November.
    11. Dung-Ying Lin & Chi Xie, 2011. "The Pareto-optimal Solution Set of the Equilibrium Network Design Problem with Multiple Commensurate Objectives," Networks and Spatial Economics, Springer, vol. 11(4), pages 727-751, December.
    12. Chi Xie & Xing Wu & Stephen Boyles, 2019. "Traffic equilibrium with a continuously distributed bound on travel weights: the rise of range anxiety and mental account," Annals of Operations Research, Springer, vol. 273(1), pages 279-310, February.
    13. Ma, Jie & Xu, Min & Meng, Qiang & Cheng, Lin, 2020. "Ridesharing user equilibrium problem under OD-based surge pricing strategy," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 1-24.
    14. Xu, Zhandong & Chen, Anthony & Li, Guoyuan & Li, Zhengyang & Liu, Xiaobo, 2024. "Elastic-demand bi-criteria traffic assignment under the continuously distributed value of time: A two-stage gradient projection algorithm with graphical interpretations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 183(C).
    15. Wang, Judith Y.T. & Ehrgott, Matthias & Chen, Anthony, 2014. "A bi-objective user equilibrium model of travel time reliability in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 4-15.
    16. Chen, Peng & Nie, Yu (Marco), 2013. "Bicriterion shortest path problem with a general nonadditive cost," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 419-435.
    17. O’Neill, Sam & Bagdasar, Ovidiu & Berry, Stuart & Popovici, Nicolae & Raja, Ramachandran, 2022. "Modelling equilibrium for a multi-criteria selfish routing network equilibrium flow problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 658-669.
    18. Khani, Alireza & Boyles, Stephen D., 2015. "An exact algorithm for the mean–standard deviation shortest path problem," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 252-266.
    19. Hongli Xu & Hai Yang & Jing Zhou & Yafeng Yin, 2017. "A Route Choice Model with Context-Dependent Value of Time," Transportation Science, INFORMS, vol. 51(2), pages 536-548, May.
    20. Yang, Hai & Tang, Wilson H. & Man Cheung, Wing & Meng, Qiang, 2002. "Profitability and welfare gain of private toll roads in a network with heterogeneous users," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(6), pages 537-554, July.

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