In Section I, the basic model of SDT is described with reference to a driver approaching a grade crossing with a train also approaching. The driver's task is to decide if he can cross the tracks safely or if he must stop. The treatment employs some mathematics, which can be omitted without losing the sense of the model. In describing the basic model, it becomes apparent that accident rates for different types of grade crossings are predicted by the SDT model to vary with train frequency. Section II examines accident rates at grade crossings and develops a Poisson process model of accident probability with reference to the frequency of trains and cars at grade crossings. The Poisson model predicts maximal accident rates and is useful for evaluating the effectiveness of different grade crossing devices in preventing accidents. The maximal accident rate concept is also used in Section III in applying SDT to a quantitative analysis of grade crossing devices. Section IV examines the implications of the SDT analysis for various schemes to improve grade crossing safety, contrasts the SDT model with existing models of accident prediction, and suggests areas of research which can be implemented to achieve Goal # 2 of the RDV Action Plan for Grade Crossings: Improve our understanding and knowledge of motorist behavior at grade crossings in causing collisions between trains and motor vehicles - including: 1) detection, recognition, perception and comprehension of warning devices and trains; and 2) decision making, perception of collision risk, and motivation involved in circumvention of active warning devices - in order to improve upon design, deployment and operation of grade crossing protection devices. Section V models the performance of an ideal motorist who uses information concerning the distances of his vehicle and the train from the intersection to determine whether to cross the intersection or to stop. Visual search with and without auditory localization (train horn) is incorporated into the model.