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Unconstrained weibit stochastic user equilibrium model with extensions

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  • Kitthamkesorn, Songyot
  • Chen, Anthony

Abstract

This study provides an unconstrained minimization program as an alternative formulation for the multinomial weibit (MNW) stochastic user equilibrium (SUE) model that explicitly considers the heterogeneous perception variances with respect to different trip lengths under congested conditions. Qualitative properties of the unconstrained minimization program are given to establish the equivalency and uniqueness of the MNW-SUE solution. The advantage of the unconstrained minimization programming formulation is that it allows the development of a link-based algorithm, which obviates path storage and enumeration. The methodological contributions lie in the derivation of the expected perceived travel cost (or the satisfaction function) that enables the development of an unconstrained MNW-SUE minimization program and a link-based stochastic loading mechanism combined with recent advances in line search strategies in the link-based algorithm. Numerical examples are also provided to illustrate the features of the MNW-SUE model and the link-based algorithm along with several extensions for future research.

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  • Kitthamkesorn, Songyot & Chen, Anthony, 2014. "Unconstrained weibit stochastic user equilibrium model with extensions," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 1-21.
    • Handle: RePEc:eee:transb:v:59:y:2014:i:c:p:1-21
    DOI: 10.1016/j.trb.2013.10.010
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    6. Songyot Kitthamkesorn & Anthony Chen & Sathaporn Opasanon & Suwicha Jaita, 2021. "A P-Hub Location Problem for Determining Park-and-Ride Facility Locations with the Weibit-Based Choice Model," Sustainability, MDPI, vol. 13(14), pages 1-16, July.
    7. Xu, Xiangdong & Chen, Anthony & Kitthamkesorn, Songyot & Yang, Hai & Lo, Hong K., 2015. "Modeling absolute and relative cost differences in stochastic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 686-703.
    8. Chikaraishi, Makoto & Nakayama, Shoichiro, 2016. "Discrete choice models with q-product random utilities," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 576-595.
    9. Chen, Anthony & Choi, Keechoo, 2017. "Solving the combined modal split and traffic assignment problem with two types of transit impedance functionAuthor-Name: Ryu, Seungkyu," European Journal of Operational Research, Elsevier, vol. 257(3), pages 870-880.
    10. Kitthamkesorn, Songyot & Chen, Anthony, 2017. "Alternate weibit-based model for assessing green transport systems with combined mode and route travel choices," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 291-310.
    11. Watling, David Paul & Rasmussen, Thomas Kjær & Prato, Carlo Giacomo & Nielsen, Otto Anker, 2015. "Stochastic user equilibrium with equilibrated choice sets: Part I – Model formulations under alternative distributions and restrictions," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 166-181.
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    13. Rasmussen, Thomas Kjær & Watling, David Paul & Prato, Carlo Giacomo & Nielsen, Otto Anker, 2015. "Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 146-165.
    14. Ryu, Seungkyu & Chen, Anthony & Michael Zhang, H. & Recker, Will, 2014. "Path flow estimator for planning applications in small communities," Transportation Research Part A: Policy and Practice, Elsevier, vol. 69(C), pages 212-242.
    15. Tinessa, Fiore, 2021. "Closed-form random utility models with mixture distributions of random utilities: Exploring finite mixtures of qGEV models," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 262-288.
    16. Xie, J. & Wong, S.C. & Zhan, S. & Lo, S.M. & Chen, Anthony, 2020. "Train schedule optimization based on schedule-based stochastic passenger assignment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 136(C).
    17. Ji, Xiangfeng & Chu, Yanyu, 2020. "A target-oriented bi-attribute user equilibrium model with travelers’ perception errors on the tolled traffic network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 144(C).
    18. Du, Muqing & Tan, Heqing & Chen, Anthony, 2021. "A faster path-based algorithm with Barzilai-Borwein step size for solving stochastic traffic equilibrium models," European Journal of Operational Research, Elsevier, vol. 290(3), pages 982-999.
    19. Li, Guoyuan & Chen, Anthony, 2023. "Strategy-based transit stochastic user equilibrium model with capacity and number-of-transfers constraints," European Journal of Operational Research, Elsevier, vol. 305(1), pages 164-183.
    20. Ampol Karoonsoontawong & Dung-Ying Lin, 2015. "Combined Gravity Model Trip Distribution and Paired Combinatorial Logit Stochastic User Equilibrium Problem," Networks and Spatial Economics, Springer, vol. 15(4), pages 1011-1048, December.
    21. Yao, Jia & Chen, Anthony, 2014. "An analysis of logit and weibit route choices in stochastic assignment paradox," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 31-49.
    22. Gu, Yu & Chen, Anthony & Kitthamkesorn, Songyot, 2022. "Weibit choice models: Properties, mode choice application and graphical illustrations," Journal of choice modelling, Elsevier, vol. 44(C).
    23. Shao, Hu & Lam, William H.K. & Sumalee, Agachai & Chen, Anthony & Hazelton, Martin L., 2014. "Estimation of mean and covariance of peak hour origin–destination demands from day-to-day traffic counts," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 52-75.
    24. Jonathan Corcoran & Sui Tao, 2017. "Mapping spatial patterns of bus usage under varying local temperature conditions," Journal of Maps, Taylor & Francis Journals, vol. 13(1), pages 74-81, January.
    25. Nakayama, Shoichiro & Chikaraishi, Makoto, 2015. "Unified closed-form expression of logit and weibit and its extension to a transportation network equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 672-685.

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