The tolerable waiting time: A generalized Pareto distribution model with empirical investigation

[Display omitted] •We investigated pedestrian waiting times at countdown and conventional signalized intersections.•The generalized Pareto distribution (GPD) method was applied to model the field data.•Various estimators of GPD parameters were studied using Monte Carlo simulations.•Pedestrian waiting times with various quantiles were predicted.•Pedestrians tend to wait longer before violating the traffic signal at intersections with a countdown signal. In China, it is more common for pedestrians than vehicles to disobey traffic signals, resulting in a high risk of pedestrian-vehicle accidents. Pedestrian waiting time are the most critical indicator of the tendency to violate traffic signals. A statistical analysis based on 4027 field-collected samples showed that the length of time that pedestrians are prepared to wait depends on the type of pedestrian traffic signal. Compared to a countdown-type signal, pedestrians were more likely to violate conventional-type signals. Furthermore, pedestrians were willing to wait longer during peak hours than during off-peak hours. There were no significant differences between the waiting times of male and female travelers. To predict pedestrian waiting time, we propose a generalized Pareto distribution (GPD) model and calibrated it based on our field data. Monte Carlo simulations showed that the maximum likelihood estimation (MLE), Bayesian MLE (BMLE), and weighted nonlinear least squares (WNLS) models are the best methods for estimating the scale and shape parameters of the GPD model. Several empirical results were output from the models. For example, at countdown-type signals, the 85th quantile of the tolerable waiting time in off-peak and peak hours was 51.5 and 54.4 s, respectively; the respective values for males and females were 55.4 and 55.0 s. At conventional signals, the tolerable waiting time was approximately 42.5 s. These findings are useful for the planning, design, and operation of pedestrian facilities.