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A Stochastic Differential Equation Framework for Modeling Queue Length Dynamics Inspired by Self-Similarity

Shakib Mustavee et al.

IEEE Transactions on Intelligent Transportation Systems2026https://doi.org/10.1109/tits.2026.3676353article
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Abstract

This article proposes a stochastic differential equation (SDE) to model the temporal evolution of queue length dynamics at signalized intersections. Motivated by the observed quasiperiodicity, long-range dependence, and self-similar characteristics of queue length time series, the proposed model incorporates these three features into the SDE through: (i) a periodic mean-reversion term to capture quasiperiodicity, (ii) a multiplicative noise term, and (iii) a fractional Brownian motion (fBm) to capture self-similarity and long-range dependence. Model parameters are estimated directly from data using a particle-filter–based likelihood framework. Using the extracted parameters, the model is applied to one-step-ahead prediction of queue lengths at four signalized intersections along a traffic corridor in Orlando, Florida. The proposed gray-box approach achieves error metrics that are better than those obtained with an LSTM-based predictor, despite using substantially fewer training samples. In addition to prediction accuracy, the model reproduces key statistical properties of the observed data, including a $1/f$ -type power spectral density and closely matching probability distributions. The results demonstrate that the proposed SDE and particle-filtering framework provides a data-efficient, interpretable approach for modeling and predicting queue dynamics at signalized intersections.

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https://doi.org/https://doi.org/10.1109/tits.2026.3676353

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@article{shakib2026,
  title        = {{A Stochastic Differential Equation Framework for Modeling Queue Length Dynamics Inspired by Self-Similarity}},
  author       = {Shakib Mustavee et al.},
  journal      = {IEEE Transactions on Intelligent Transportation Systems},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1109/tits.2026.3676353},
}

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A Stochastic Differential Equation Framework for Modeling Queue Length Dynamics Inspired by Self-Similarity

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Evidence weight

0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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