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Stochastic User Equilibrium Model with a Bounded Perceived Travel Time

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  • Songyot Kitthamkesorn
  • Anthony Chen

Abstract

Stochastic User Equilibrium (SUE) models depict the perception differences in traffic assignment problems. According to the assumption of an unbounded perceived travel time distribution, the conventional SUE problems result in a positive choice probability for all available routes, regardless of their unappealing travel time. This study provides an eUnit-SUE model to relax this assumption. The eUnit model is derived from a bounded probability distribution. This closed-form model aligns with an exponentiated random utility maximization (ERUM) paradigm with the exponentiated uniform distributed random error, where the lower and upper bounds endogeneously determine the route usage. Specifically, a Beckmann-type mathematical programming formulation is presented for the eUnit-SUE problem. The equivalency and uniqueness properties are rigorously proven. Numerical examples reveal that the eUnit bound range between the lower and upper bounds greatly affects the SUE assignment results. A larger bound range increases not only the number of routes in the choice set but also the degree of dispersion in the assignment results due to a larger route-specific perception variance. The misperception is contingent upon the disparity between the shortest and longest travel times and the bounds. As the bound range decreases, the shortest route receives significant flow allocation, and the assignment result approaches the deterministic user equilibrium (DUE) flow pattern.

Suggested Citation

  • Songyot Kitthamkesorn & Anthony Chen, 2024. "Stochastic User Equilibrium Model with a Bounded Perceived Travel Time," Papers 2402.18435, arXiv.org.
    • Handle: RePEc:arx:papers:2402.18435
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    References listed on IDEAS

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    1. Kitthamkesorn, Songyot & Chen, Anthony, 2013. "A path-size weibit stochastic user equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 378-397.
    2. Wang, Guangchao & Chen, Anthony & Kitthamkesorn, Songyot & Ryu, Seungkyu & Qi, Hang & Song, Ziqi & Song, Jianguo, 2020. "A multi-modal network equilibrium model with captive mode choice and path size logit route choice," Transportation Research Part A: Policy and Practice, Elsevier, vol. 136(C), pages 293-317.
    3. 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.
    4. 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.
    5. Jayakrishnan, R. & Tsai, Wei T. & Prashker, Joseph N. & Rajadhyaksha, Subodh, 1994. "A Faster Path-Based Algorithm for Traffic Assignment," University of California Transportation Center, Working Papers qt2hf4541x, University of California Transportation Center.
    6. Leemis, Lawrence M. & McQueston, Jacquelyn T., 2008. "Univariate Distribution Relationships," The American Statistician, American Statistical Association, vol. 62, pages 45-53, February.
    7. Leurent, Fabien M., 1997. "Curbing the computational difficulty of the logit equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 315-326, August.
    8. 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.
    9. 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).
    10. Shlomo Bekhor & Moshe Ben-Akiva & M. Ramming, 2006. "Evaluation of choice set generation algorithms for route choice models," Annals of Operations Research, Springer, vol. 144(1), pages 235-247, April.
    11. 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.
    12. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    13. Li, Baibing, 2011. "The multinomial logit model revisited: A semi-parametric approach in discrete choice analysis," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 461-473, March.
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