Solomon curve 2020: Relating microscopic risk models with accident statistics

Traffic accident statistics as functions of the involved accident parameters are important sources of information to investigate accident causes. However, since traffic accidents are sparse events and the factors that lead to an accident can be very diverse, it is difficult to establish a direct link which relates microscopic risk models to the empirical findings. One seminal and widely debated work on accident statistics on multi-lane roadways is given by the so-called “Solomon curve” [1], which describes the collision rate of automobiles as a function of their speed. While one particular characteristic of the Solomon curve - its u-shape - has been explained theoretically in terms of traffic flow of passing cars in [2], a detailed derivation from microscopic risk models is still missing. In this paper, we start from a first-principles generalized risk model, and reconfirm the explanation of the curve, revealing that its parameters can be fully mapped to the parameters of the underlying microscopic risk model. In addition, an unexplained effect of the Solomon curve - the asymmetry of its minimum with respect to the average velocity - is predicted and explained by the derivation. The result then is two-fold: On one hand, we can now fully understand the Solomon curve in terms of microscopic risk parameters, and on the other hand, the empirical findings of the Solomon curve serve as a validation of the risk model and can be used to gain reasonable settings for microscopic risk parameters.