Abstract This study proposes an optimized GM(0,N) model that integrates entry traffic volume, conflicting flow, and signal timing (green and red times) for predicting queue lengths at metered roundabouts. While conventional GM models have the advantage of requiring few samples and offering high prediction accuracy, they can lead to prediction errors as they do not consider the influence of other factors on time series. To enhance prediction accuracy, the proposed model transforms the original sequence by combining exponential and trigonometric functions to overcome the limitations of single transformation functions in processing original sequences and the difficulty of fixed transformation functions adapting to various data types. Optimal parameters are then determined using PSO. This model was validated using real-world data obtained from metered roundabouts in Adelaide, Australia. Compared to An’s model, as well as the GM(1,1), GM(1,N), and conventional GM(0,N) models, the proposed method demonstrated superior accuracy across MRE, RMSE, MAE, and box plot analyses. These results support the model’s applicability for managing unbalanced roundabout traffic and for effective detector placement.
An et al. (2026) studied this question.