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Travel time estimation based on piecewise truncated quadratic speed trajectory

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  • Sun, Lu
  • Yang, Jun
  • Mahmassani, Hani

Abstract

A piecewise truncated quadratic speed trajectory is proposed to mimic the unknown speed trajectory between point detectors. The basis functions of the new method consist of quadratic and constant functions of time. The constant functions, corresponding to upper and lower speed bounds, are determined using the maximum likelihood estimates of highest and lowest speeds that have been historically observed within a time interval. The purpose of setting a lower (upper) speed bound for simulating vehicle speed trajectory is to mimic a low (high) average speed during transition flow and congestion, and to restrict a quadratic speed trajectory to be within a realistic speed range, respectively. It was found that travel time estimation using different approaches is similar during free-flow conditions but significantly different during transition flow and congestion conditions. Using the actual travel time obtained from field experiment, the new method yields more accurate travel time estimation than other trajectory-based methods. Compared to travel time estimation using speed and density information, the new method only needs speed measurements, and therefore, it is more robust and easier to implement in practice than density-based methods. Computational implementation of the new trajectory method is tractable and can be done very efficiently, making it suitable for on-line real time travel time estimation.

Suggested Citation

  • Sun, Lu & Yang, Jun & Mahmassani, Hani, 2008. "Travel time estimation based on piecewise truncated quadratic speed trajectory," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(1), pages 173-186, January.
    • Handle: RePEc:eee:transa:v:42:y:2008:i:1:p:173-186
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    References listed on IDEAS

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    1. Dailey, D. J., 1999. "A statistical algorithm for estimating speed from single loop volume and occupancy measurements," Transportation Research Part B: Methodological, Elsevier, vol. 33(5), pages 313-322, June.
    2. Dailey, D. J., 1993. "Travel-time estimation using cross-correlation techniques," Transportation Research Part B: Methodological, Elsevier, vol. 27(2), pages 97-107, April.
    3. Petty, Karl F. & Bickel, Peter & Ostland, Michael & Rice, John & Schoenberg, Frederic & Jiang, Jiming & Ritov, Ya'acov, 1998. "Accurate estimation of travel times from single-loop detectors," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(1), pages 1-17, January.
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    2. Nantes, Alfredo & Ngoduy, Dong & Miska, Marc & Chung, Edward, 2015. "Probabilistic travel time progression and its application to automatic vehicle identification data," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 131-145.
    3. Celikoglu, Hilmi Berk, 2013. "Reconstructing freeway travel times with a simplified network flow model alternating the adopted fundamental diagram," European Journal of Operational Research, Elsevier, vol. 228(2), pages 457-466.
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    5. Sun, Lu & Jafaripournimchahi, Ammar & Kornhauser, Alain & Hu, Wushen, 2020. "A new higher-order viscous continuum traffic flow model considering driver memory in the era of autonomous and connected vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    6. Wörz, Sascha & Bernhardt, Heinz, 2017. "A novel method for optimal fuel consumption estimation and planning for transportation systems," Energy, Elsevier, vol. 120(C), pages 565-572.

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