Improved grey system models for predicting traffic parameters

Comert, Gurcan; Begashaw, Negash; Huynh, Nathan · 2021 · Crossref

DOI: 10.1016/j.eswa.2021.114972

archive: archived pipeline: cataloged verified

Get this paper ↗ (DOI — opens at the source; we link to it, we don't host it)

Summary

This study addresses the challenge of accurate short-term traffic parameter prediction, which is critical for transportation applications such as real-time route guidance, ramp metering, and congestion pricing. Existing time series models often struggle with the nonlinear, stochastic, and non-stationary nature of traffic flow, particularly during abrupt changes caused by incidents. To overcome these limitations, the authors propose three novel online Grey system models (GM) augmented with trigonometric and exponential functions: GM(1,1|cos(ωt)), GM(1,1|sin(ωt), cos(ωt)), and GM(1,1|e−at ,sin(ωt),cos(ωt)). These models are designed to better capture oscillating behaviors and abrupt changes in traffic data while requiring minimal training data. The researchers evaluated the proposed models against a suite of benchmark models, including the standard GM(1,1), Grey Verhulst models (with and without Fourier error corrections), linear time series models, and nonlinear time series models. The evaluation utilized four distinct datasets collected from loop detectors and GPS-based probe vehicles in California, Virginia, and Oregon. These datasets covered various traffic parameters, including speed, travel time, volume, and occupancy, under both normal and abnormal (incident-affected) conditions. The benchmark models were trained on initial data series, while the proposed Grey models were optimized using grid search for frequency parameters. Notably, the study found that only four observations were sufficient for training the proposed models. The results demonstrated that the proposed models significantly outperformed the benchmarks. Among the benchmark group, the error-corrected Grey Verhulst model with Fourier corrections performed best, surpassing the standard GM(1,1) and time series models. However, the three proposed models exceeded the Grey Verhulst model’s performance substantially. Specifically, GM(1,1|cos(ωt)) improved prediction accuracy by 65% in Root Mean Squared Error (RMSE) and 82% in Mean Absolute Percentage Error (MAPE). GM(1,1|sin(ωt), cos(ωt)) showed improvements of 16% in RMSE and 58% in MAPE, while GM(1,1|e−at ,sin(ωt),cos(ωt)) achieved gains of 11% in RMSE and 42% in MAPE. The significance of this work lies in the development of highly adaptive, data-efficient models for traffic forecasting. The proposed Grey system models proved robust across different roadway types and traffic parameters, maintaining high accuracy even during abnormal traffic fluctuations. Their ability to deliver precise predictions with minimal data requirements makes them particularly suitable for real-time traffic management systems where data availability may be limited or where rapid adaptation to changing conditions is essential. This study contributes to the literature by validating the effectiveness of incorporating trigonometric and exponential terms into Grey models for short-term traffic estimation.

Provenance

The full processing record for this entry. Every stage of this paper's journey through the pipeline is logged — what ran, with which tool and model, how many attempts it took, and when it last completed.

Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.

Topics

Ranked by relevance to this paper. Hover a topic for its definition.

• mental model of traffic