Modeling Dynamics of Dilemma Zones by Formulating Dynamical Contributing Factors with Video-observed Trajectory Data

Abstract

The dynamics of the dilemma zone (DZ) have been realized since the concept of the dilemma zone was proposed in 1960. The dynamics are a reflection of the dynamical characteristics of the driver-vehicle complex, and can be characterized by the dynamical features of the dilemma zone contributing factors which include the minimum perception-reaction time (PRT) and the maximum deceleration and acceleration rates. To date, the dynamics of these contributing factors have not yet been well modeled and quantified despite being continuously explored by researchers over decades. In the absence of the quantitative knowledge about these contributing factors, the dilemma zone with assumed constant parameter values, and the Type II dilemma zone defined from a probabilistic perspective (i.e. a zone in which at the onset of yellow interval more than 10% and less than 90% drivers would choose to stop) were widely used in practice as alternatives in estimating the dilemma zone. However, both alternatives are compromised in ways, being still incapable of reflecting the dilemma zone dynamics. In fact, the incapacity of modeling and quantifying the dilemma zone dynamics was due to the lack of reliable and robust vehicular trajectory data during the yellow intervals. The availability of video-capture based software VEVID enabled the collection of high-frequency time-based trajectory data from high-definition digital video and hence offered technical preparedness for modeling the dilemma zone dynamics. The most significant innovation of this paper lies in the proposal of the dynamical dilemma zone model by incorporating the quantitative dynamics into the traditional dilemma zone model. The dynamical contributing factors were identified, quantified, and eventually formulated. Particularly, the models for the contributing factors were developed and validated using separate datasets. The validation results indicated that the models for the dynamical contributing factors are effective in predicting the minimum PRT and the maximum acceleration and deceleration rates under various speed conditions. Specifically, the minimum PRT is a function of individual vehicle's speed; and the maximum deceleration and acceleration rates are functions of both the individual vehicle's speed and the intersection approach's 85th percentile speed. The final evaluation compared the dynamical dilemma zone with the traditional dilemma zone model, and the Type II dilemma zone model calibrated based on the same trajectory data used for developing the dynamical dilemma zone model. As expected, the evaluation results indicated that the dynamical dilemma zone model estimated the dilemma zone more accurately than the traditional dilemma zone model and the Type II dilemma zone model. This innovation brings advancement in empirical understanding and theoretical modeling of the dynamics of DZ and hence provides theoretical support for developing more efficient and effective dilemma zone protection strategies in the future.