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On the calibration of stochastic car following models

Author

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  • Zhou, Shirui
  • Zheng, Shiteng
  • Xu, Tu
  • Treiber, Martin
  • Tian, Junfang
  • Jiang, Rui

Abstract

Recent empirical and theoretical findings highlight the critical role of stochasticity in car-following (CF) dynamics. Although several stochastic CF models have been proposed, their calibration remains relatively underexplored compared to deterministic models. This article addresses this gap by utilizing four stochastic CF models to conduct a comprehensive evaluation of two existing calibration methods—minimizing multiple runs mean error (MRMean) and maximum likelihood estimation (MLE) as well as a newly proposed method, minimizing multiple runs minimum (MRMin) error, based on synthetic trajectories. Results show that MRMean and MLE exhibit significant biases in estimating the ground truth values of stochastic model parameters, while MRMin achieves nearly zero estimation errors. Specifically, MRMean eliminates stochasticity, transforming models into deterministic ones, whereas MRMin successfully separates aleatoric errors caused by randomness and epistemic errors caused by parameters, as demonstrated through a theoretical error analysis. Furthermore, CF experiments conducted in an identical driving environment reveal that differences in spacing are more pronounced than differences in speed. Calibration against experimental trajectories verifies the conclusions drawn from synthetic trajectories and theoretical analysis. Additionally, the covariance matrix of parameters is estimated using bootstrap sampling, highlighting MRMin’s ability to capture the inherent stochasticity of CF behavior. These findings deepen our understanding of CF stochasticity and provide a robust framework for calibrating stochastic models.

Suggested Citation

  • Zhou, Shirui & Zheng, Shiteng & Xu, Tu & Treiber, Martin & Tian, Junfang & Jiang, Rui, 2025. "On the calibration of stochastic car following models," Transportation Research Part B: Methodological, Elsevier, vol. 196(C).
  • Handle: RePEc:eee:transb:v:196:y:2025:i:c:s0191261525000736
    DOI: 10.1016/j.trb.2025.103224
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    References listed on IDEAS

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    1. Ngoduy, D., 2021. "Noise-induced instability of a class of stochastic higher order continuum traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 260-278.
    2. Sharma, Anshuman & Zheng, Zuduo & Bhaskar, Ashish, 2019. "Is more always better? The impact of vehicular trajectory completeness on car-following model calibration and validation," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 49-75.
    3. Tian, Junfang & Jiang, Rui & Jia, Bin & Gao, Ziyou & Ma, Shoufeng, 2016. "Empirical analysis and simulation of the concave growth pattern of traffic oscillations," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 338-354.
    4. Zheng, Shi-Teng & Jiang, Rui & Tian, Jun-Fang & Zhang, H.M. & Li, Zhen-Hua & Gao, Lan-Da & Jia, Bin, 2021. "Experimental study on properties of lightly congested flow," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 1-19.
    5. Laval, Jorge A. & Toth, Christopher S. & Zhou, Yi, 2014. "A parsimonious model for the formation of oscillations in car-following models," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 228-238.
    6. G. F. Newell, 2002. "Memoirs on Highway Traffic Flow Theory in the 1950s," Operations Research, INFORMS, vol. 50(1), pages 173-178, February.
    7. Tian, Junfang & Zhang, H.M. & Treiber, Martin & Jiang, Rui & Gao, Zi-You & Jia, Bin, 2019. "On the role of speed adaptation and spacing indifference in traffic instability: Evidence from car-following experiments and its stochastic model," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 334-350.
    8. repec:plo:pone00:0094351 is not listed on IDEAS
    9. Tian, Junfang & Treiber, Martin & Ma, Shoufeng & Jia, Bin & Zhang, Wenyi, 2015. "Microscopic driving theory with oscillatory congested states: Model and empirical verification," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 138-157.
    10. Punzo, Vincenzo & Montanino, Marcello, 2016. "Speed or spacing? Cumulative variables, and convolution of model errors and time in traffic flow models validation and calibration," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 21-33.
    11. Taylor, Jeffrey & Zhou, Xuesong & Rouphail, Nagui M. & Porter, Richard J., 2015. "Method for investigating intradriver heterogeneity using vehicle trajectory data: A Dynamic Time Warping approach," Transportation Research Part B: Methodological, Elsevier, vol. 73(C), pages 59-80.
    12. Treiber, Martin & Kanagaraj, Venkatesan, 2015. "Comparing numerical integration schemes for time-continuous car-following models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 183-195.
    13. Jiang, Rui & Hu, Mao-Bin & Zhang, H.M. & Gao, Zi-You & Jia, Bin & Wu, Qing-Song, 2015. "On some experimental features of car-following behavior and how to model them," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 338-354.
    14. Tian, Junfang & Li, Guangyu & Treiber, Martin & Jiang, Rui & Jia, Ning & Ma, Shoufeng, 2016. "Cellular automaton model simulating spatiotemporal patterns, phase transitions and concave growth pattern of oscillations in traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 560-575.
    15. Xu, Tu & Laval, Jorge, 2020. "Statistical inference for two-regime stochastic car-following models," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 210-228.
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