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An Efficient Algorithm for Real-Time Estimation and Prediction of Dynamic OD Tables

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  • M. Bierlaire

    (EPFL, CH-1015 Lausanne, Switzerland)

  • F. Crittin

    (EPFL, CH-1015 Lausanne, Switzerland)

Abstract

The problem of estimating and predicting Origin-Destination (OD) tables is known to be important and difficult. In the specific context of Intelligent Transportation Systems (ITS), the dynamic nature of the problem and the real-time requirements make it even more intricate.We consider here a least-square modeling approach for solving the OD estimation and prediction problem, which seems to offer convenient and flexible algorithms. The dynamic nature of the problem is represented by an autoregressive process, capturing the serial correlations of the state variables. Our formulation is inspired from Cascetta et al. (1993) and Ashok and Ben-Akiva (1993). We compare the Kalman filter algorithm to LSQR, an iterative algorithm proposed by Paige and Saunders (1982) for the solution of large-scale least-squares problems. LSQR explicitly exploits matrix sparsity, allowing to consider larger problems likely to occur in real applications.We show that the LSQR algorithm significantly decreases the computation effort needed by the Kalman filter approach for large-scale problems. We also provide a theoretical number of flops for both algorithms to predict which algorithm will perform better on a specific instance of the problem.

Suggested Citation

  • M. Bierlaire & F. Crittin, 2004. "An Efficient Algorithm for Real-Time Estimation and Prediction of Dynamic OD Tables," Operations Research, INFORMS, vol. 52(1), pages 116-127, February.
    • Handle: RePEc:inm:oropre:v:52:y:2004:i:1:p:116-127
    DOI: 10.1287/opre.1030.0071
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    References listed on IDEAS

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    1. 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.
    2. Okutani, Iwao & Stephanedes, Yorgos J., 1984. "Dynamic prediction of traffic volume through Kalman filtering theory," Transportation Research Part B: Methodological, Elsevier, vol. 18(1), pages 1-11, February.
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    4. K. Ashok & M. E. Ben-Akiva, 2000. "Alternative Approaches for Real-Time Estimation and Prediction of Time-Dependent Origin–Destination Flows," Transportation Science, INFORMS, vol. 34(1), pages 21-36, February.
    5. Van Zuylen, Henk J. & Willumsen, Luis G., 1980. "The most likely trip matrix estimated from traffic counts," Transportation Research Part B: Methodological, Elsevier, vol. 14(3), pages 281-293, September.
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    Cited by:

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    2. Chao Sun & Yulin Chang & Xin Luan & Qiang Tu & Wenyun Tang, 2020. "Origin-Destination Demand Reconstruction Using Observed Travel Time under Congested Network," Networks and Spatial Economics, Springer, vol. 20(3), pages 733-755, September.
    3. Tangjian Wei & Feng Shi & Guangming Xu, 2019. "Estimation of Time-Varying Passenger Demand for High Speed Rail System," Complexity, Hindawi, vol. 2019, pages 1-24, March.
    4. Kumarage, Sakitha & Yildirimoglu, Mehmet & Zheng, Zuduo, 2023. "A hybrid modelling framework for the estimation of dynamic origin–destination flows," Transportation Research Part B: Methodological, Elsevier, vol. 176(C).
    5. 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.
    6. Yusen Chen & Henk J. van Zuylen & Wim van der Hoeven, 2010. "A Large-scale Urban Traffic Decision Support System with Dynamic Traffic Assignment," Chapters, in: Chris M.J. Tampere & Francesco Viti & Lambertus H. (Ben) Immers (ed.), New Developments in Transport Planning, chapter 17, Edward Elgar Publishing.
    7. Cantelmo, Guido & Qurashi, Moeid & Prakash, A. Arun & Antoniou, Constantinos & Viti, Francesco, 2020. "Incorporating trip chaining within online demand estimation," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 171-187.
    8. 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.
    9. Bierlaire, M. & Crittin, F. & Themans, M., 2007. "A multi-iterate method to solve systems of nonlinear equations," European Journal of Operational Research, Elsevier, vol. 183(1), pages 20-41, November.
    10. Yong Lin, 2023. "Models, Algorithms and Applications of DynasTIM Real-Time Traffic Simulation System," Sustainability, MDPI, vol. 15(2), pages 1-30, January.
    11. Osorio, Carolina, 2019. "High-dimensional offline origin-destination (OD) demand calibration for stochastic traffic simulators of large-scale road networks," Transportation Research Part B: Methodological, Elsevier, vol. 124(C), pages 18-43.

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