Traffic Density versus Rear-End Crash Risk on Freeways: Empirical Model, Mechanism Model, and Transfer to Automated Vehicles

The statistical models supporting the Highway Safety Manual quantify associations between aggregate traffic measures, such as average daily traffic volume or posted speed limit, and crash frequencies accumulated over several years. For some time though, it has been recognized that crash risk can vary as traffic conditions vary due to special events or within-day changes in traffic. Additionally, the Highway Safety Manual's predictive tools are essentially statistical summaries of conditions present during the recent past, and transferring this knowledge to environments containing automated vehicles is likely to be problematic. This paper illustrates how both issues can be addressed by supplementing standard statistical modeling with models describing crash mechanisms. In particular, Brill's random walk model of how traffic shockwaves generate rear-end crashes is combined with a traffic flow model based on a fundamental diagram in order to quantify the relation between traffic density and rear-end crash risk. Approximating Brill's random walk with a finite Markov chain leads to a computationally tractable model, and the model's predicted relationship is consistent with empirical findings. Transferring the model to a hypothetical environment with automated vehicles is then illustrated.