Investigating pedestrian waiting time at semi-controlled crossing locations: Application of multi-state models for recurrent events analysis.

"Semi-controlled" crosswalks are unsignalized, but clearly marked with "yield to pedestrian within crosswalk" signs. Ideally, pedestrians can cross the street immediately after they arrive at the curb. However, real world observations show that pedestrians and vehicles are often involved in non-verbal "negotiations" to decide who should proceed first. This kind of "negotiation" often causes delays for both parties and may lead to unsafe situations. The study in this paper was based on video recordings of the waiting behaviors of 2059 pedestrians interacting with 1003 motorists at selected semi-controlled crosswalks. One such location experienced a conversion from one-way operation to two-way operation, which provided a rare opportunity for a before-and-after study at that location. Multi-state Markov models were introduced as a novel approach to correlate the dynamic process between recurrent events. Time-varying covariates related to pedestrian characteristics, traffic condition, and vehicle dynamics (distance and speed) turned out to be significant. The analytical method developed in this study provides a tool to dynamically model pedestrian waiting decisions with uncertainties. Model results reveal that, after the conversion from one-way to two-way operation, the probability of a pedestrian accepting a lag decreases from 69.7% to just below 60% on the same street. In addition, pedestrians are more hesitant to cross a two-way street than a one-way street. Countermeasures that increase motorist yielding rate or reduce pedestrian confusion will enhance safety such crossing locations.