Three methods for estimating a range of vehicular interactions

Abstract We present three different approaches how to estimate the number of preceding cars influencing a decision-making procedure of a given driver moving in saturated traffic flows. The first method is based on correlation analysis, the second one evaluates (quantitatively) deviations from the main assumption in the convolution theorem for probability, and the third one operates with advanced instruments of the theory of counting processes (statistical rigidity). We demonstrate that universally-accepted premise on short-ranged traffic interactions may not be correct. All methods introduced have revealed that minimum number of actively-followed vehicles is two. It supports an actual idea that vehicular interactions are, in fact, middle-ranged. Furthermore, consistency between the estimations used is surprisingly credible. In all cases we have found that the interaction range (the number of actively-followed vehicles) drops with traffic density. Whereas drivers moving in congested regimes with lower density (around 30 vehicles per kilometer) react on four or five neighbors, drivers moving in high-density flows respond to two predecessors only.