IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v53y2019i3p665-682.html
   My bibliography  Save this article

Unbiased Estimation Methods of Nonlinear Transport Models Based on Linearly Projected Data

Author

Listed:
  • Wai Wong

    (Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, Michigan 48109; Department of Civil Engineering, University of Hong Kong, Pokfulam, Hong Kong)

  • S. C. Wong

    (Department of Civil Engineering, University of Hong Kong, Pokfulam, Hong Kong)

Abstract

Linear data projection is widely used for unbiased traffic data estimation. Nevertheless, recent studies have proven that direct model estimation based on linearly projected data that ignores the scaling factor variability may lead to systematically biased parameters. Adjustment factors were derived for a generalised multivariate polynomial (GMP) function with fixed exponents to remove such biases. However, the methods have not been extended to generic nonlinear transport models necessitating nonlinear regressions. This paper scrutinises the mechanism of systematic data point distortion resulting from linear data projection and identifies the practical difficulties of the adjustment factor approach to other nonlinear models. To reduce such biases in nonlinear transport models, a generic mean value restoration (MVR) method, requiring only the first two moments of the scaling factor, and an extended MVR (EMVR) method, further incorporating higher-order moments by assuming a scaling factor distribution, are proposed. Simulation studies are conducted for both GMP functions with relaxed exponents and multivariate exponential decay functions, which are the most commonly adopted nonlinear functions for modeling traffic flow, to examine the effectiveness and robustness of the proposed methods for recovering the assumed true model parameters. Results reveal that the EMVR method generally can achieve higher level of accuracy.

Suggested Citation

  • Wai Wong & S. C. Wong, 2019. "Unbiased Estimation Methods of Nonlinear Transport Models Based on Linearly Projected Data," Transportation Science, INFORMS, vol. 53(3), pages 665-682, May.
    • Handle: RePEc:inm:ortrsc:v:53:y:2019:i:3:p:665-682
    DOI: 10.1287/trsc.2018.0856
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/trsc.2018.0856
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.2018.0856?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
    ---><---

    References listed on IDEAS

    as
    1. Saeedmanesh, Mohammadreza & Geroliminis, Nikolas, 2017. "Dynamic clustering and propagation of congestion in heterogeneously congested urban traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 193-211.
    2. Wong, Wai & Wong, S.C., 2015. "Systematic bias in transport model calibration arising from the variability of linear data projection," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 1-18.
    3. Geroliminis, Nikolas & Daganzo, Carlos F., 2008. "Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 759-770, November.
    4. Herrera, Juan C. & Bayen, Alexandre M., 2010. "Incorporation of Lagrangian measurements in freeway traffic state estimation," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 460-481, May.
    5. Daganzo, Carlos F., 2007. "Corrigendum to "Urban gridlock: Macroscopic modeling and mitigation approaches" [Transportation Research Part B 41 (2007) 49-62]," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 379-379, March.
    6. Nikolas Geroliminis & David M. Levinson, 2009. "Cordon Pricing Consistent with the Physics of Overcrowding," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 219-240, Springer.
    7. John, Wright & Dahlgren, Joy, 2001. "Using Vehicles Equipped with Toll Tags as Probes for Providing Travel Times," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt9f17h2j0, Institute of Transportation Studies, UC Berkeley.
    8. Zheng, Nan & Waraich, Rashid A. & Axhausen, Kay W. & Geroliminis, Nikolas, 2012. "A dynamic cordon pricing scheme combining the Macroscopic Fundamental Diagram and an agent-based traffic model," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(8), pages 1291-1303.
    9. Saeedmanesh, Mohammadreza & Geroliminis, Nikolas, 2016. "Clustering of heterogeneous networks with directional flows based on “Snake” similarities," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 250-269.
    10. Moore, II, James E. & Cho, Seongkil & Basu, Arup & Mezger, Daniel B., 2001. "Use of Los Angeles Freeway Service Patrol Vehicles as Probe Vehicles," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt8qf8430v, Institute of Transportation Studies, UC Berkeley.
    11. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peng, Jiali & Shangguan, Wei & Peng, Cong & Chai, Linguo, 2024. "Uncertainty modeling of connected and automated vehicle penetration rate under mixed traffic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 639(C).
    2. Wong, Wai & Shen, Shengyin & Zhao, Yan & Liu, Henry X., 2019. "On the estimation of connected vehicle penetration rate based on single-source connected vehicle data," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 169-191.

    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. Zheng, Nan & Geroliminis, Nikolas, 2020. "Area-based equitable pricing strategies for multimodal urban networks with heterogeneous users," Transportation Research Part A: Policy and Practice, Elsevier, vol. 136(C), pages 357-374.
    2. Wong, Wai & Wong, S.C., 2016. "Biased standard error estimations in transport model calibration due to heteroscedasticity arising from the variability of linear data projection," Transportation Research Part B: Methodological, Elsevier, vol. 88(C), pages 72-92.
    3. S. F. A. Batista & Ludovic Leclercq, 2019. "Regional Dynamic Traffic Assignment Framework for Macroscopic Fundamental Diagram Multi-regions Models," Transportation Science, INFORMS, vol. 53(6), pages 1563-1590, November.
    4. Yildirimoglu, Mehmet & Sirmatel, Isik Ilber & Geroliminis, Nikolas, 2018. "Hierarchical control of heterogeneous large-scale urban road networks via path assignment and regional route guidance," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 106-123.
    5. Dantsuji, Takao & Takayama, Yuki & Fukuda, Daisuke, 2023. "Perimeter control in a mixed bimodal bathtub model," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 267-291.
    6. Chen, Zhi & Wu, Wen-Xiang & Huang, Hai-Jun & Shang, Hua-Yan, 2022. "Modeling traffic dynamics in periphery-downtown urban networks combining Vickrey's theory with Macroscopic Fundamental Diagram: user equilibrium, system optimum, and cordon pricing," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 278-303.
    7. Tang, Siyi & Zheng, Fangfang & Zheng, Nan & Liu, Xiaobo, 2024. "An efficient multi-modal urban transportation network partitioning approach for three-dimensional macroscopic fundamental diagram," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    8. Amirgholy, Mahyar & Gao, H. Oliver, 2017. "Modeling the dynamics of congestion in large urban networks using the macroscopic fundamental diagram: User equilibrium, system optimum, and pricing strategies," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 215-237.
    9. Ge, Qian & Fukuda, Daisuke, 2019. "A macroscopic dynamic network loading model for multiple-reservoir system," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 502-527.
    10. Daganzo, Carlos F. & Lehe, Lewis J., 2015. "Distance-dependent congestion pricing for downtown zones," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 89-99.
    11. Ding, Heng & Di, Yunran & Feng, Zhongxiang & Zhang, Weihua & Zheng, Xiaoyan & Yang, Tao, 2022. "A perimeter control method for a congested urban road network with dynamic and variable ranges," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 160-187.
    12. Daganzo, Carlos F & Lehe, Lewis J, 2014. "Distance-dependent Congestion Pricing for Downtown Zones," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt9vz1b9rs, Institute of Transportation Studies, UC Berkeley.
    13. Zhong, R.X. & Huang, Y.P. & Chen, C. & Lam, W.H.K. & Xu, D.B. & Sumalee, A., 2018. "Boundary conditions and behavior of the macroscopic fundamental diagram based network traffic dynamics: A control systems perspective," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 327-355.
    14. Batista, S.F.A. & Leclercq, Ludovic & Geroliminis, Nikolas, 2019. "Estimation of regional trip length distributions for the calibration of the aggregated network traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 192-217.
    15. Gayah, Vikash V. & Gao, Xueyu (Shirley) & Nagle, Andrew S., 2014. "On the impacts of locally adaptive signal control on urban network stability and the Macroscopic Fundamental Diagram," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 255-268.
    16. Gao, Shengling & Li, Daqing & Zheng, Nan & Hu, Ruiqi & She, Zhikun, 2022. "Resilient perimeter control for hyper-congested two-region networks with MFD dynamics," Transportation Research Part B: Methodological, Elsevier, vol. 156(C), pages 50-75.
    17. Yao, Wenbin & Chen, Nuo & Su, Hongyang & Hu, Youwei & Jin, Sheng & Rong, Donglei, 2023. "A novel self-adaption macroscopic fundamental diagram considering network heterogeneity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 613(C).
    18. Loder, Allister & Bliemer, Michiel C.J. & Axhausen, Kay W., 2022. "Optimal pricing and investment in a multi-modal city — Introducing a macroscopic network design problem based on the MFD," Transportation Research Part A: Policy and Practice, Elsevier, vol. 156(C), pages 113-132.
    19. Gao, Xueyu (Shirley) & Gayah, Vikash V., 2018. "An analytical framework to model uncertainty in urban network dynamics using Macroscopic Fundamental Diagrams," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 660-675.
    20. Wong, Wai & Wong, S.C., 2015. "Systematic bias in transport model calibration arising from the variability of linear data projection," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 1-18.

    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:inm:ortrsc:v:53:y:2019:i:3:p:665-682. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.