  We have studied the distribution of traffic flow $q$ for the
Nagel-Schreckenberg model by computer simulations. We applied a large-deviation
approach, which allowed us to obtain the distribution $P(q)$ over more than one
hundred decades in probability, down to probabilities like $10^{-140}$. This
allowed us to characterize the flow distribution over a large range of the
support and identify the characteristics of rare and even very rare traffic
situations. We observe a change of the distribution shape when increasing the
density of cars from the free flow to the congestion phase. Furthermore, we
characterize typical and rare traffic situations by measuring correlations of
$q$ to other quantities like density of standing cars or number and size of
traffic jams.
