Real-Time Traffic Flow Uncertainty Quantification Based on Non-Parametric Probability Density Function Estimation

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.