  We consider a small stochastic perturbation of an optimal velocity
car-following model. We give a detailed analysis of behavior near the collision
singularity. We show that collision is impossible in a simplified model without
noise, and then we show that collision is asymptotically unlikely over large
time intervals in presence of small noise, with large time interval scaling
like a square of the reciprocal of the strength of the noise. Our calculations
depend on careful boundary-layer analyses.
