  This study explores the hypothesis that an analytically derived estimate of
the required driver reaction time for asymptotic stability, based on the
macroscopic Gazis, Herman, and Rothery (GHR) model, can serve as an effective
indicator of the impact of traffic oscillations on rear-end crashes. If
separate GHR models are fit discontinuously for the uncongested and congested
regimes, the local drop in required reaction time between the two regimes can
also be estimated. This study evaluates the relationship between freeway
rear-end crash rates and this drop in driver reaction time.
  Traffic data from 28 sensors collected over one year were used to calibrate
the two-regime GHR model. Rear-end crash rates for the segments surrounding the
sensor locations are estimated using archived crash data over four years. The
rear-end crash rates exhibited a strong positive correlation with the reaction
time drop at the density-breakpoint of the congested regime. A linear form
model provided the best fit in terms of R-square, standard error, and
homoscedasticity. These results motivate follow-on research to incorporate
macroscopically derived reaction time in road-safety planning. More generally,
the study demonstrates a useful application of a discontinuous macroscopic
traffic model.
