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

Gary A. Davis, Indrajit Chatterjee, Jingru Gao, John Hourdos

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Article number04021007
JournalJournal of Transportation Engineering Part A: Systems
Issue number4
StatePublished - Apr 1 2021

Bibliographical note

Funding Information:
This research was supported in part by the Minnesota DOT. The authors would like to thank Raphael Stern for his insight and guidance regarding the ACC models in the section “Transferring Knowledge to an AV Environment.”

Publisher Copyright:
© 2021 This work is made available under the terms of the Creative Commons Attribution 4.0 International license,.


  • Adaptive cruise control
  • Automatic emergency braking
  • Driver reaction time
  • Fundamental diagram
  • Random walk
  • Rear-end crashes
  • Shockwaves


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