IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v181y2010i1p709-72210.1007-s10479-010-0784-0.html
   My bibliography  Save this article

Optimal linear estimator of origin-destination flows with redundant data

Author

Listed:
  • Frédéric Meunier

Abstract

Suppose given a network endowed with a multiflow. We want to estimate some quantities connected with this multiflow, for instance the value of an s–t flow for one of the sources–sinks pairs s–t, but only measures on some arcs are available, at least on one s–t cocycle (set of arcs having exactly one endpoint in a subset X of vertices with s∈X and t∉X). These measures, supposed to be unbiased, are random variables whose variances are known. How can we combine them optimally in order to get the best estimator of the value of the s–t flow? This question arises in practical situations when the OD matrix of a transportation network must be estimated. We will give a complete answer for the case when we deal with linear combinations, not only for the value of an s–t flow but also for any quantity depending linearly from the multiflow. Interestingly, we will see that the Laplacian matrix of the network plays a central role. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • Frédéric Meunier, 2010. "Optimal linear estimator of origin-destination flows with redundant data," Annals of Operations Research, Springer, vol. 181(1), pages 709-722, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:709-722:10.1007/s10479-010-0784-0
    DOI: 10.1007/s10479-010-0784-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-010-0784-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-010-0784-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cascetta, Ennio & Nguyen, Sang, 1988. "A unified framework for estimating or updating origin/destination matrices from traffic counts," Transportation Research Part B: Methodological, Elsevier, vol. 22(6), pages 437-455, December.
    2. Bierlaire, M. & Toint, Ph. L., 1995. "Meuse: An origin-destination matrix estimator that exploits structure," Transportation Research Part B: Methodological, Elsevier, vol. 29(1), pages 47-60, February.
    3. Spiess, Heinz, 1987. "A maximum likelihood model for estimating origin-destination matrices," Transportation Research Part B: Methodological, Elsevier, vol. 21(5), pages 395-412, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Michel Bierlaire & Frank Crittin, 2006. "Solving Noisy, Large-Scale Fixed-Point Problems and Systems of Nonlinear Equations," Transportation Science, INFORMS, vol. 40(1), pages 44-63, February.
    4. Walpen, Jorgelina & Mancinelli, Elina M. & Lotito, Pablo A., 2015. "A heuristic for the OD matrix adjustment problem in a congested transport network," European Journal of Operational Research, Elsevier, vol. 242(3), pages 807-819.
    5. Flurin S. Hänseler & Nicholas A. Molyneaux & Michel Bierlaire, 2017. "Estimation of Pedestrian Origin-Destination Demand in Train Stations," Transportation Science, INFORMS, vol. 51(3), pages 981-997, August.
    6. 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.
    7. Martin, Peter T., 1995. "Turning Movement Estimation In Real Time (TMERT)," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3rp1v8fs, Institute of Transportation Studies, UC Berkeley.
    8. Juha-Matti Kuusinen & Janne Sorsa & Marja-Liisa Siikonen, 2015. "The Elevator Trip Origin-Destination Matrix Estimation Problem," Transportation Science, INFORMS, vol. 49(3), pages 559-576, August.
    9. Maryam Abareshi & Mehdi Zaferanieh & Mohammad Reza Safi, 2019. "Origin-Destination Matrix Estimation Problem in a Markov Chain Approach," Networks and Spatial Economics, Springer, vol. 19(4), pages 1069-1096, December.
    10. Fu, Hao & Lam, William H.K. & Shao, Hu & Ma, Wei & Chen, Bi Yu & Ho, H.W., 2022. "Optimization of multi-type sensor locations for simultaneous estimation of origin-destination demands and link travel times with covariance effects," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 19-47.
    11. 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.
    12. Tao Li, 2017. "A Demand Estimator Based on a Nested Logit Model," Transportation Science, INFORMS, vol. 51(3), pages 918-930, August.
    13. Yang, Yudi & Fan, Yueyue & Wets, Roger J.B., 2018. "Stochastic travel demand estimation: Improving network identifiability using multi-day observation sets," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 192-211.
    14. T. Abrahamsson, 1998. "Estimation of Origin-Destination Matrices Using Traffic Counts- A Literature Survey," Working Papers ir98021, International Institute for Applied Systems Analysis.
    15. Menon, Aditya Krishna & Cai, Chen & Wang, Weihong & Wen, Tao & Chen, Fang, 2015. "Fine-grained OD estimation with automated zoning and sparsity regularisation," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 150-172.
    16. Bielli, Maurizio & Reverberi, Pierfrancesco, 1996. "New operations research and artificial intelligence approaches to traffic engineering problems," European Journal of Operational Research, Elsevier, vol. 92(3), pages 550-572, August.
    17. Bierlaire, M. & Toint, Ph. L., 1995. "Meuse: An origin-destination matrix estimator that exploits structure," Transportation Research Part B: Methodological, Elsevier, vol. 29(1), pages 47-60, February.
    18. Hazelton, Martin L., 2001. "Inference for origin-destination matrices: estimation, prediction and reconstruction," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 667-676, August.
    19. Seungkyu Ryu, 2020. "A Bicycle Origin–Destination Matrix Estimation Based on a Two-Stage Procedure," Sustainability, MDPI, vol. 12(7), pages 1-14, April.
    20. Louis Grange & Felipe González & Shlomo Bekhor, 2017. "Path Flow and Trip Matrix Estimation Using Link Flow Density," Networks and Spatial Economics, Springer, vol. 17(1), pages 173-195, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:709-722:10.1007/s10479-010-0784-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.