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Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family

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  • Rasmussen, Thomas Kjær
  • Watling, David Paul
  • Prato, Carlo Giacomo
  • Nielsen, Otto Anker

Abstract

We propose a new class of path-based solution algorithms to solve the Restricted Stochastic User Equilibrium (RSUE), as introduced in Watling et al. (2015). The class allows a flexible specification of how the choice sets are systematically grown by considering congestion effects and how the flows are allocated among routes. The specification allows adapting traditional path-based stochastic user equilibrium flow allocation methods (originally designed for pre-specified choice sets) to the generic solution algorithm. We also propose a cost transformation function and show that by using this we can, for certain Logit-type choice models, modify existing path-based Deterministic User Equilibrium solution methods to compute RSUE solutions. The transformation function also leads to a two-part relative gap measure for consistently monitoring convergence to a RSUE solution. Numerical tests are reported on two real-life cases, in which we explore convergence patterns and choice set composition and size, for alternative specifications of the RSUE model and solution algorithm.

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  • 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.
    • Handle: RePEc:eee:transb:v:77:y:2015:i:c:p:146-165
    DOI: 10.1016/j.trb.2015.03.009
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    Cited by:

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    2. Guido Gentile, 2018. "New Formulations of the Stochastic User Equilibrium with Logit Route Choice as an Extension of the Deterministic Model," Service Science, INFORMS, vol. 52(6), pages 1531-1547, December.
    3. Ma, Jie & Meng, Qiang & Cheng, Lin & Liu, Zhiyuan, 2022. "General stochastic ridesharing user equilibrium problem with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 162(C), pages 162-194.
    4. Watling, David Paul & Rasmussen, Thomas Kjær & Prato, Carlo Giacomo & Nielsen, Otto Anker, 2018. "Stochastic user equilibrium with a bounded choice model," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 254-280.
    5. Tan, Heqing & Xu, Xiangdong & Chen, Anthony, 2024. "On endogenously distinguishing inactive paths in stochastic user equilibrium: A convex programming approach with a truncated path choice model," Transportation Research Part B: Methodological, Elsevier, vol. 183(C).
    6. Sun, S. & Szeto, W.Y., 2018. "Logit-based transit assignment: Approach-based formulation and paradox revisit," Transportation Research Part B: Methodological, Elsevier, vol. 112(C), pages 191-215.
    7. 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.
    8. Larsen, Rune & Rich, Jeppe & Rasmussen, Thomas Kjær, 2019. "Hub-based truck platooning: Potentials and profitability," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 127(C), pages 249-264.
    9. Jiang, Y. & Szeto, W.Y., 2016. "Reliability-based stochastic transit assignment: Formulations and capacity paradox," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 181-206.

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