IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v596y2022ics0378437122001285.html
   My bibliography  Save this article

Spatio-temporal modelling and prediction of bus travel time using a higher-order traffic flow model

Author

Listed:
  • Bharathi, Dhivya
  • Vanajakshi, Lelitha
  • Subramanian, Shankar C.

Abstract

Accurate bus travel time prediction in real-time is challenging, as numerous factors such as fluctuating travel demand, incidents, signals, bus stops, dwell times, and seasonal variations can affect travel time, a spatio-temporal variable. Literature that considered the spatio-temporal evolution of bus travel time adopting traffic flow theory-based models investigated one-equation models (also widely known as first-order model) predominantly while the two-equation models (commonly known as higher-order models) have not been sufficiently explored due to their complex structure, parameters to calibrate, hardship in obtaining the data, and difficulty in discretizing and solving. Motivated by this, the present study explores the suitability of higher order traffic flow models for the prediction of bus travel time. This study adopted a well-known two-equation model ‘Aw-Rascle model‘ (Aw and Rascle, 2000), which addressed most of the limitations of the previous models, and discretized using a Finite volume method to preserve the conservational properties of Partial Differential Equations (PDE). As Global Positioning System (GPS) is a widespread data source for transit systems, the identified model was rewritten in terms of speed by adopting a suitable pressure function. The discretized model was represented in the state-state-space form and integrated with a filtering technique using appropriate inputs, to facilitate real-time implementation. The performance of the proposed methodology was evaluated and compared with a first order model (Lighthill Whittam Richards (LWR) model) based approach to understand the efficacy of the higher-order models in travel time prediction. The prediction accuracy in terms of Mean Absolute Percentage Error (MAPE) was around 14% for the proposed methodology with an absolute deviation of around +/-1.2 min, which was better than the existing LWR model-based prediction method. The developed real-time prediction methodology is a promising one to be integrated with Advanced Public Transportation Systems (APTS) applications.

Suggested Citation

  • Bharathi, Dhivya & Vanajakshi, Lelitha & Subramanian, Shankar C., 2022. "Spatio-temporal modelling and prediction of bus travel time using a higher-order traffic flow model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    • Handle: RePEc:eee:phsmap:v:596:y:2022:i:c:s0378437122001285
    DOI: 10.1016/j.physa.2022.127086
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437122001285
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2022.127086?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. Jiang, Rui & Wu, Qing-Song & Zhu, Zuo-Jin, 2002. "A new continuum model for traffic flow and numerical tests," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 405-419, June.
    2. Boel, René & Mihaylova, Lyudmila, 2006. "A compositional stochastic model for real time freeway traffic simulation," Transportation Research Part B: Methodological, Elsevier, vol. 40(4), pages 319-334, May.
    3. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    4. Papageorgiou, Markos, 1998. "Some remarks on macroscopic traffic flow modelling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(5), pages 323-329, September.
    5. Sanwal, Kumud K. & Petty, Karl & Walrand, Jean & Fawaz, Youssef, 1996. "An extended macroscopic model for traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 30(1), pages 1-9, February.
    6. Zhang, H. M., 2002. "A non-equilibrium traffic model devoid of gas-like behavior," Transportation Research Part B: Methodological, Elsevier, vol. 36(3), pages 275-290, March.
    7. Serin, Faruk & Alisan, Yigit & Kece, Adnan, 2021. "Hybrid time series forecasting methods for travel time prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 579(C).
    8. Daganzo, Carlos F., 1995. "Requiem for second-order fluid approximations of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 277-286, August.
    9. Long, Jiancheng & Gao, Ziyou & Szeto, W.Y., 2011. "Discretised link travel time models based on cumulative flows: Formulations and properties," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 232-254, January.
    10. S. P. Anusha & R. A. Anand & L. Vanajakshi, 2012. "Data Fusion Based Hybrid Approach for the Estimation of Urban Arterial Travel Time," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, September.
    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. Xie, Minghui & Zhang, Xinying & Wu, Zhouhao & Wei, Sen & Gao, Yanan & Wang, Yuanqing, 2023. "A shared parking optimization framework based on dynamic resource allocation and path planning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    2. Shao, Feng & Shao, Hu & Wang, Dongle & Lam, William H.K., 2024. "A multi-task spatio-temporal generative adversarial network for prediction of travel time reliability in peak hour periods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 638(C).

    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. Mohammadian, Saeed & Zheng, Zuduo & Haque, Md. Mazharul & Bhaskar, Ashish, 2021. "Performance of continuum models for realworld traffic flows: Comprehensive benchmarking," Transportation Research Part B: Methodological, Elsevier, vol. 147(C), pages 132-167.
    2. Mohan, Ranju & Ramadurai, Gitakrishnan, 2021. "Multi-class traffic flow model based on three dimensional flow–concentration surface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).
    3. Tang, Tie-Qiao & Shi, Wei-Fang & Huang, Hai-Jun & Wu, Wen-Xiang & Song, Ziqi, 2019. "A route-based traffic flow model accounting for interruption factors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 767-785.
    4. Yaroslav Kholodov & Andrey Alekseenko & Viktor Kazorin & Alexander Kurzhanskiy, 2021. "Generalization Second Order Macroscopic Traffic Models via Relative Velocity of the Congestion Propagation," Mathematics, MDPI, vol. 9(16), pages 1-14, August.
    5. Blandin, Sébastien & Argote, Juan & Bayen, Alexandre M. & Work, Daniel B., 2013. "Phase transition model of non-stationary traffic flow: Definition, properties and solution method," Transportation Research Part B: Methodological, Elsevier, vol. 52(C), pages 31-55.
    6. Raadsen, Mark P.H. & Bliemer, Michiel C.J. & Bell, Michael G.H., 2016. "An efficient and exact event-based algorithm for solving simplified first order dynamic network loading problems in continuous time," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 191-210.
    7. Salim Mammar & Jean-Patrick Lebacque & Habib Haj Salem, 2009. "Riemann Problem Resolution and Godunov Scheme for the Aw-Rascle-Zhang Model," Transportation Science, INFORMS, vol. 43(4), pages 531-545, November.
    8. Mohammadian, Saeed & Zheng, Zuduo & Haque, Mazharul & Bhaskar, Ashish, 2023. "NET-RAT: Non-equilibrium traffic model based on risk allostasis theory," Transportation Research Part A: Policy and Practice, Elsevier, vol. 174(C).
    9. Zhai, Cong & Wu, Weitiao, 2022. "A continuum model considering the uncertain velocity of preceding vehicles on gradient highways," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    10. Bouadi, Marouane & Jia, Bin & Jiang, Rui & Li, Xingang & Gao, Zi-You, 2022. "Stability analysis of stochastic second-order macroscopic continuum models and numerical simulations," Transportation Research Part B: Methodological, Elsevier, vol. 164(C), pages 193-209.
    11. Fan, De-li & Zhang, Yi-cai & Shi, Yin & Xue, Yu & Wei, Fang-ping, 2018. "An extended continuum traffic model with the consideration of the optimal velocity difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 402-413.
    12. Yuan, Yun & Zhang, Zhao & Yang, Xianfeng Terry & Zhe, Shandian, 2021. "Macroscopic traffic flow modeling with physics regularized Gaussian process: A new insight into machine learning applications in transportation," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 88-110.
    13. Gabriel Obed Fosu & Francis Tabi Oduro & Carlo Caligaris, 2021. "Multilane analysis of a viscous second-order macroscopic traffic flow model," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-17, February.
    14. Jin, Wen-Long, 2016. "On the equivalence between continuum and car-following models of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 543-559.
    15. Sun, Fengxin & Wang, Jufeng & Cheng, Rongjun, 2019. "An improved anisotropic continuum model considering the driver’s desire for steady driving," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1449-1462.
    16. Ranju Mohan & Gitakrishnan Ramadurai, 2015. "Submission to the DTA2012 Special Issue: A Case for Higher-Order Traffic Flow Models in DTA," Networks and Spatial Economics, Springer, vol. 15(3), pages 765-790, September.
    17. Peng, Guanghan & Xu, Mingzuo & Tan, Huili, 2024. "Phase transition in a new heterogeneous macro continuum model of traffic flow under rain and snow weather environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    18. Corli, Andrea & Fan, Haitao, 2023. "String stability in traffic flows," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    19. Zheng, Liang & Jin, Peter J. & Huang, Helai, 2015. "An anisotropic continuum model considering bi-directional information impact," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 36-57.
    20. Carey, Malachy & Bar-Gera, Hillel & Watling, David & Balijepalli, Chandra, 2014. "Implementing first-in–first-out in the cell transmission model for networks," Transportation Research Part B: Methodological, Elsevier, vol. 65(C), pages 105-118.

    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:eee:phsmap:v:596:y:2022:i:c:s0378437122001285. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.