We consider an optimal-velocity car-following model with reaction-time delay of drivers, where the characteristics of the drivers change according to a suitably calibrated random walk. In the absence of this stochasticity we find stable and almost stable oscillations that correspond to stop-and-go traffic jams that eventually merge or disperse. We study how the distribution of the merging times depends on the parameters of the random walk. Our numerical simulations suggest that the motion of the fronts into and out of traffic jams may be subject to a `macroscopic' random walk
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