A Statistics Based Approach for Defining Reference Trajectories on Road Sections

Theories and models usually adopted in designing roads, especially for safety verifications, are based on the hypothesis of a single vehicle that follows a trajectory matching with the road axle. This condition can be expressed as "road following" model and it determines many important design parameters, like curvature, design speed, superelevation, lane placement, sight distances, characteristics of transition curves, etc.. In real conditions, vehicles on a road section travel along trajectories always different from the road axle, so, in order to ensure that theoretical models can be effective, it is important to evaluate how a reference trajectory, on particular road elements, can statistically represent the population of users. In this way, it will be possible to design the road axle on the basis of this reference trajectory and consequently develop road design processes. To deal with these problems, it is useful to perform some surveys on trajectories of vehicles on real road elements, but the statistical analysis of the data needs specific procedures to extract trajectories that have a formal geometric expression and correctly represent the scattering of vehicles' position. The article presents a statistics based method, proposed with the aim to obtain the reference trajectories on road sections starting from surveys over real exercise conditions; the method was tested on case studies regarding two ramp terminals, that are particularly interesting because when the infrastructure present special geometrical or physical features the vehicle trajectories are influenced by them