Comparative assessment of safety indicators for vehicle trajectories on the highway

Safety measurement and analysis have been a challenging and well-researched topic in transportation. Conventionally, surrogate safety measures have been used as safety indicators in simulation models for safety assessment, in control formulations for driver assistance systems, and in data analysis of naturalistic driving studies. However, surrogate indicators only give partial insights into traffic safety i.e., they only indicate a predetermined set of possible pre-crash situations for an interacting vehicle pair. Recently, a safety indicator called the driving safety field based on field theory has been proposed for two-dimensional vehicle interactions. However, the objectivity of its functional form and validity are yet to be tested. This paper provides a qualitative and quantitative comparison of different safety indicators as a risk measure to demarcate their mathematical properties and evaluate their usefulness in quantifying trajectory risk. We compare five relevant safety indicators: inverse time to collision, post-encroachment time, potential indicator of collision with urgent decceleration, warning index and safety field strength. Their formulations are mathematically analyzed to yield qualitative insights and their values over simulated vehicle trajectories are evaluated to yield quantitative insights. Our results acknowledge the limitations and demarcate the functional utilities of the selected safety indicators.