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Prism-based path set restriction for solving Markovian traffic assignment problem

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  • Oyama, Yuki
  • Hato, Eiji

Abstract

This paper deals with a main limitation of Markovian traffic assignment (MTA) models: when the network includes cyclic structures and the link costs are small enough, the fact that the MTA models assign traffic flows to all feasible paths causes computational challenges. This study addresses this issue by proposing a method of restricting path set based on the concept of choice-based prism. To achieve a prism-based path set, a novel network description and the constraints are introduced. These are flexible and compatible with the MTA operation, meaning that our method does not extinguish the mathematical and computational advantages of the MTA models. Our network description allows the expected minimum cost to take a value specific for each state, or a pair of node and choice-stage. This enables us to perform traffic assignment with a simple solution procedure, regardless of parameter setting or network structure. The numerical experiments show that our method solves the computational challenges of the MTA models and that the incorporation of the prism constraints does not increase computational effort required, or rather, it is computationally efficient even when considering the correlation among path utilities.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:transb:v:122:y:2019:i:c:p:528-546
    DOI: 10.1016/j.trb.2019.02.002
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    Cited by:

    1. Leleux, Pierre & Courtain, Sylvain & Françoisse, Kevin & Saerens, Marco, 2022. "Design of biased random walks on a graph with application to collaborative recommendation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    2. Yuki Oyama, 2023. "Global path preference and local response: A reward decomposition approach for network path choice analysis in the presence of locally perceived attributes," Papers 2307.08646, arXiv.org.
    3. Mogens Fosgerau & Nikolaj Nielsen & Mads Paulsen & Thomas Kj{ae}r Rasmussen & Rui Yao, 2024. "Substitution in the perturbed utility route choice model," Papers 2409.08347, arXiv.org.
    4. Oyama, Yuki, 2024. "Global path preference and local response: A reward decomposition approach for network path choice analysis in the presence of visually perceived attributes," Transportation Research Part A: Policy and Practice, Elsevier, vol. 181(C).
    5. 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.
    6. Yuki Oyama, 2022. "Capturing positive network attributes during the estimation of recursive logit models: A prism-based approach," Papers 2204.01215, arXiv.org, revised Jan 2023.

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