Estimating gap acceptance parameters with a Bayesian approach

Abstract

The gap acceptance framework is the theoretical basis for modelling traffic flow at intersections with a priority control. Reliable estimation methods for key gap acceptance parameters are important to more accurately predict key traffic performance measures such as capacity and delay. A notable challenge is that the critical gaps are not directly observable. Currently, the maximum likelihood estimator (MLE) is widely accepted as the most reliable method. In this research, we considered a Bayesian approach as an alternative framework for estimating gap acceptance parameters, which achieves a comparable performance to the MLE. We first formalised the gap acceptance statistical model and the estimand of interest, based on a Bayesian hierarchical formulation that naturally captures the variations between drivers. We then tested the performance of each method on simulated dataset, with the Bayesian posterior obtained through the No-U-Turn sampler, an adaptive Markov chain Monte Carlo algorithm. We showed that the MLE and the posterior mean as a point summary of the full posterior distribution have comparable performance, and both generally achieve a mean absolute error $\le 0.2$ s for different major stream flow $q_p$ in our experiment setup. In addition, we found that the standard error is higher for both low and high $q_p$ so any point estimator is unlikely to be equally reliable across all level of $q_p$’s. Furthermore, we also identified a potential issue when assuming consistent drivers and log-normally distributed critical gaps at high $q_p$, as the heavy tail of the log-normal can result in unrealistic dataset. The full Bayesian approach also allows inherent uncertainty quantification, which we found to be well-calibrated, in the sense that the credible intervals obtained have roughly the correct frequentist coverage as per confidence intervals constructed with frequentist methods. From a traffic engineering point of view, quantifying uncertainties in gap acceptance parameters, whether using Bayesian or frequentist methods, is important as they induce uncertainties on intersection performance metrics such as capacity and delay, which will allow more informed decision-making for infrastructure investment. In addition, we also assessed the performance of Bayesian methods for more complicated statistical models, using a test scenario involving inconsistent driver behaviour, by jointly estimating the gap acceptance parameters and the inconsistency parameters. Lastly, we demonstrated the applicability of the proposed Bayesian framework to real data collected at roundabouts in Perth, Western Australia. We found the mean critical gap to mostly lie between 3.0 to 5.0 s, and the standard deviation between 1.0 to 2.0 s, and our validation checks suggest the potential need to extend the statistical model with consideration of the interactive nature of roundabouts.