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Decomposition of Path Choice Entropy in General Transport Networks

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  • Takashi Akamatsu

    (Department of Knowledge-Based Information Engineering, Toyohashi University of Technology, Toyohashi, Aichi 441, Japan)

Abstract

This paper shows that the LOGIT type stochastic assignment/stochastic user equilibrium assignment can be represented as an optimization problem with only link variables. The conventional entropy function defined by path flows in the objective can be decomposed into a function consisting only of link flows. The idea of the decomposed formulation is derived from a consideration of the most likely link flow patterns over a network. Then the equivalence of the decomposed formulation to LOGIT assignment is proved by using the Markov properties that underlie Dial's algorithm. Through the analyses, some useful properties of the entropy function and its conjugate dual function (expected minimum cost function) have been derived. Finally, it is discussed that the derived results have a potential impact on the development of efficient algorithms for the stochastic user equilibrium assignment.

Suggested Citation

  • Takashi Akamatsu, 1997. "Decomposition of Path Choice Entropy in General Transport Networks," Transportation Science, INFORMS, vol. 31(4), pages 349-362, November.
    • Handle: RePEc:inm:ortrsc:v:31:y:1997:i:4:p:349-362
    DOI: 10.1287/trsc.31.4.349
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    Cited by:

    1. Liu, Zhiyuan & Wang, Shuaian & Meng, Qiang, 2014. "Optimal joint distance and time toll for cordon-based congestion pricing," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 81-97.
    2. Huang, Hai-Jun & Bell, Michael G. H., 1998. "A study on logit assignment which excludes all cyclic flows," Transportation Research Part B: Methodological, Elsevier, vol. 32(6), pages 401-412, August.
    3. Jun Xie & Yu (Marco) Nie, 2019. "A New Algorithm for Achieving Proportionality in User Equilibrium Traffic Assignment," Transportation Science, INFORMS, vol. 53(2), pages 566-584, March.
    4. Raadsen, Mark P.H. & Bliemer, Michiel C.J. & Bell, Michael G.H., 2020. "Aggregation, disaggregation and decomposition methods in traffic assignment: historical perspectives and new trends," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 199-223.
    5. Zhiyuan Liu & Wen Yi & Shuaian Wang & Jun Chen, 2017. "On the Uniqueness of User Equilibrium Flow with Speed Limit," Networks and Spatial Economics, Springer, vol. 17(3), pages 763-775, September.
    6. Oyama, Yuki & Hara, Yusuke & Akamatsu, Takashi, 2022. "Markovian traffic equilibrium assignment based on network generalized extreme value model," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 135-159.
    7. Paul Koster & Erik T. Verhoef & Simon Shepherd & David Watling, 2014. "Probabilistic Choice and Congestion Pricing with Heterogeneous Travellers and Price-Sensitive Demand," Tinbergen Institute Discussion Papers 14-078/VIII, Tinbergen Institute, revised 13 Nov 2014.
    8. Kumar, Amit & Peeta, Srinivas, 2015. "Entropy weighted average method for the determination of a single representative path flow solution for the static user equilibrium traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 213-229.
    9. Oyama, Yuki & Hato, Eiji, 2019. "Prism-based path set restriction for solving Markovian traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 528-546.
    10. Michael Patriksson & R. Tyrrell Rockafellar, 2002. "A Mathematical Model and Descent Algorithm for Bilevel Traffic Management," Transportation Science, INFORMS, vol. 36(3), pages 271-291, August.
    11. Bar-Gera, Hillel, 2010. "Traffic assignment by paired alternative segments," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1022-1046, September.
    12. Selin Damla Ahipaşaoğlu & Uğur Arıkan & Karthik Natarajan, 2019. "Distributionally Robust Markovian Traffic Equilibrium," Transportation Science, INFORMS, vol. 53(6), pages 1546-1562, November.
    13. Jiayang Li & Qianni Wang & Liyang Feng & Jun Xie & Yu Marco Nie, 2024. "A Day-to-Day Dynamical Approach to the Most Likely User Equilibrium Problem," Papers 2401.08013, arXiv.org.
    14. Dial, Robert B., 2006. "A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration," Transportation Research Part B: Methodological, Elsevier, vol. 40(10), pages 917-936, December.
    15. Jorge Lorca & Emerson Melo, 2020. "Choice Aversion in Directed Networks," Working Papers Central Bank of Chile 879, Central Bank of Chile.
    16. François Gilbert & Patrice Marcotte & Gilles Savard, 2015. "A Numerical Study of the Logit Network Pricing Problem," Transportation Science, INFORMS, vol. 49(3), pages 706-719, August.

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