Real-Time Traffic Flow Uncertainty Quantification Based on Nonparametric Probability Density Function Estimation
Publication: Journal of Transportation Engineering, Part A: Systems
Volume 150, Issue 11
Abstract
Traffic flow uncertainty quantification is important for making reliable decisions in transportation operations. Compared with well-studied level prediction or point prediction models, the study of uncertainty quantification that can capture the second-order fluctuations of traffic observations is still in its infancy. Current traffic flow uncertainty quantification approaches can be classified in general into distribution- or nondistribution-based. For the former, generalized autoregressive conditional heteroscedasticity (GARCH) model and stochastic volatility (SV) have been widely applied to quantify traffic flow uncertainty in terms of prediction interval, usually under a parametric Gaussian distribution assumption. However, a parametric model relies on a prespecified model structure and cannot meet the requirement raised by the time-varying traffic condition patterns. Therefore, this paper proposed a real-time traffic condition uncertainty quantification approach based on a nonparametric probability density function (PDF) estimation. For this approach, the real-time nonparametric kernel density estimation method is applied to capture the time-varying probability density of traffic flow data based on which prediction intervals are constructed in real time using the quantiles computed from the estimated time-varying nonparametric PDF. Real-world traffic flow data are applied to validate the proposed approach. The results show that the proposed approach outperforms the comparative models of an online GARCH filter and three lower and upper bound estimation (LUBE) models based on multilayer perceptron (MLP), spiking neural network (SNN), and long short-term memory networks (LSTM). The findings indicate that the quantification of traffic condition uncertainty is complementary to the conventional traffic condition level modeling, and combined, traffic level modeling and traffic uncertainty quantification can support the development of proactive and reliable transportation applications.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. The available data are listed as follows: (1) thirty-six preprocessed traffic flow series shown in Table 2; (2) KP performance shown in Fig. 3; (3) WFR performance shown in Fig. 4; (4) prediction intervals generated by WKS, DKS, MLP-based LUBE, LSTM-based LUBE, SNN-based LUBE, and online GARCH filter shown in Fig. 5; and (5) estimated probability density function of residuals shown in Fig. 6.
Acknowledgments
This research is supported by the Key Laboratory of Transport Industry of Comprehensive Transportation Theory (Nanjing Modern Multimodal Transportation Laboratory), Ministry of Transport, PRC through open Project No. MTF2023005. The authors also thank the United Kingdom National Highways, Minnesota Department of Transportation, Washington State Department of Transportation, and Maryland Department of Transportation for providing the data used in this study. The results and views presented in this paper are the authors, and the authors hold all responsibility for the analyses presented in this work.
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Published In
Journal of Transportation Engineering, Part A: Systems
Volume 150 • Issue 11 • November 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jan 29, 2024
Accepted: Jun 17, 2024
Published online: Sep 9, 2024
Published in print: Nov 1, 2024
Discussion open until: Feb 9, 2025
ASCE Technical Topics:
- Continuum mechanics
- Density currents
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Fluid dynamics
- Fluid mechanics
- Hydraulic engineering
- Hydrologic engineering
- Infrastructure
- Mathematics
- Models (by type)
- Motion (dynamics)
- Parameters (statistics)
- Probability
- Solid mechanics
- Statistics
- Traffic engineering
- Traffic flow
- Traffic management
- Traffic models
- Traffic volume
- Transportation engineering
- Uncertainty principles
- Water and water resources
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