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Simultaneous Estimation of the Origin-Destination Matrices and Travel-Cost Coefficient for Congested Networks in a Stochastic User Equilibrium

Author

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  • Hai Yang

    (Department of Civil Engineering, The Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong, China)

  • Qiang Meng

    (Department of Civil Engineering, The Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong, China)

  • Michael G. H. Bell

    (Department of Civil Engineering, The University of Newcastle upon Tyne, NE1 7RU, United Kingdom)

Abstract

This article proposes an optimization model for simultaneous estimation of an origin-destination (O-D) matrix and a travel-cost coefficient for congested networks in a logit-based stochastic user equilibrium (SUE). The model is formulated in the form of a standard differentiable, nonlinear optimization problem with analytical stochastic user equilibrium constraints. Explicit expressions of the derivatives of the stochastic user equilibrium constraints with respect to origin-destination demand, link flow, and travel-cost coefficient are derived and computed efficiently through a stochastic network-loading approach. A successive quadratic-programming algorithm using the derivative information is applied to solve the simultaneous estimation model. This algorithm converges to a Karusch-Kuhn-Tucker point of the problem under certain conditions. The proposed model and algorithm are illustrated with a numerical example.

Suggested Citation

  • Hai Yang & Qiang Meng & Michael G. H. Bell, 2001. "Simultaneous Estimation of the Origin-Destination Matrices and Travel-Cost Coefficient for Congested Networks in a Stochastic User Equilibrium," Transportation Science, INFORMS, vol. 35(2), pages 107-123, May.
    • Handle: RePEc:inm:ortrsc:v:35:y:2001:i:2:p:107-123
    DOI: 10.1287/trsc.35.2.107.10133
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    References listed on IDEAS

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    Cited by:

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    3. Yang, Yudi & Fan, Yueyue & Royset, Johannes O., 2019. "Estimating probability distributions of travel demand on a congested network," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 265-286.
    4. Lo, Hing-Po & Chan, Chi-Pak, 2003. "Simultaneous estimation of an origin-destination matrix and link choice proportions using traffic counts," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(9), pages 771-788, November.
    5. Byung Chung & Hsun-Jung Cho & Terry Friesz & Henh Huang & Tao Yao, 2014. "Sensitivity Analysis of User Equilibrium Flows Revisited," Networks and Spatial Economics, Springer, vol. 14(2), pages 183-207, June.
    6. Gutjahr, Walter J. & Dzubur, Nada, 2016. "Bi-objective bilevel optimization of distribution center locations considering user equilibria," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 85(C), pages 1-22.
    7. García-Ródenas, Ricardo & Marín, Ángel, 2009. "Simultaneous estimation of the origin-destination matrices and the parameters of a nested logit model in a combined network equilibrium model," European Journal of Operational Research, Elsevier, vol. 197(1), pages 320-331, August.
    8. Doblas, Javier & Benitez, Francisco G., 2005. "An approach to estimating and updating origin-destination matrices based upon traffic counts preserving the prior structure of a survey matrix," Transportation Research Part B: Methodological, Elsevier, vol. 39(7), pages 565-591, August.
    9. Lundgren, Jan T. & Peterson, Anders, 2008. "A heuristic for the bilevel origin-destination-matrix estimation problem," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 339-354, May.
    10. Zhang, Michael & Nie, Yu & Shen, Wei & Lee, Ming S. & Jansuwan, Sarawut & Chootinan, Piya & Pravinvongvuth, Surachet & Chen, Anthony & Recker, Will W., 2008. "Development of A Path Flow Estimator for Inferring Steady-State and Time-Dependent Origin-Destination Trip Matrices," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3nr033sc, Institute of Transportation Studies, UC Berkeley.
    11. Chiou, Suh-Wen, 2005. "Bilevel programming for the continuous transport network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 39(4), pages 361-383, May.
    12. Tao Li, 2017. "A Demand Estimator Based on a Nested Logit Model," Transportation Science, INFORMS, vol. 51(3), pages 918-930, August.
    13. Caggiani, Leonardo & Camporeale, Rosalia & Ottomanelli, Michele, 2017. "Facing equity in transportation Network Design Problem: A flexible constraints based model," Transport Policy, Elsevier, vol. 55(C), pages 9-17.
    14. Zao Li & Yanyan Gao & Li Yu & Charles L. Choguill & Weiyi Cui, 2022. "Analysis of the Elderly’s Preferences for Choosing Medical Service Facilities from the Perspective of Accessibility: A Case Study of Tertiary General Hospitals in Hefei, China," IJERPH, MDPI, vol. 19(15), pages 1-23, August.
    15. Yang, Yudi & Fan, Yueyue, 2015. "Data dependent input control for origin–destination demand estimation using observability analysis," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 385-403.
    16. Z. Wu & W. Lam, 2006. "Transit passenger origin-destination estimation in congested transit networks with elastic line frequencies," Annals of Operations Research, Springer, vol. 144(1), pages 363-378, April.
    17. Bera, Sharminda & Rao, K. V. Krishna, 2011. "Estimation of origin-destination matrix from traffic counts: the state of the art," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 49, pages 2-23.
    18. Wang, Hai & Yang, Hai, 2019. "Ridesourcing systems: A framework and review," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 122-155.
    19. Yang, Chao & Chen, Anthony & Xu, Xiangdong & Wong, S.C., 2013. "Sensitivity-based uncertainty analysis of a combined travel demand model," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 225-244.

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