Calibration of stochastic link-based fundamental diagram with explicit consideration of speed heterogeneity

Abstract

This study aims to establish a stochastic link-based fundamental diagram (FD) with explicit consideration of two available sources of uncertainty: speed heterogeneity, indicated by the speed variance within an interval, and rainfall intensity. A stochastic structure was proposed to incorporate the speed heterogeneity into the traffic stream model, and the random-parameter structures were applied to reveal the unobserved heterogeneity in the mean speeds at an identical density. The proposed stochastic link-based FD was calibrated and validated using real-world traffic data obtained from two selected road segments in Hong Kong. Traffic data were obtained from the Hong Kong Journey Time Indication System operated by the Hong Kong Transport Department during January 1 to December 31, 2017. The data related to rainfall intensity were obtained from the Hong Kong Observatory. A two-stage calibration based on Bayesian inference was proposed for estimating the stochastic link-based FD parameters. The predictive performances of the proposed model and three other models were compared using K-fold cross-validation. The results suggest that the random-parameter model considering the speed heterogeneity effect performs better in terms of both goodness-of-fit and predictive accuracy. The effect of speed heterogeneity accounts for 18%–24% of the total heterogeneity effects on the variance of FD. In addition, there exists unobserved heterogeneity across the mean speeds at an identical density, and the rainfall intensity negatively affects the mean speed and its effect on the variance of FD differs at different densities.