  We consider a modified Nagel-Schreckenberg (NS) model in which drivers do not
decelerate if their speed is smaller than the headway (number of empty sites to
the car ahead). (In the original NS model, such a reduction in speed occurs
with probability $p$, independent of the headway, as long as the current speed
is greater than zero.) In the modified model the free-flow state (with all
vehicles traveling at the maximum speed, $v_{max}$) is {\it absorbing} for
densities $\rho$ smaller than a critical value $\rho_c = 1/(v_{max} + 2)$. The
phase diagram in the $\rho - p$ plane is reentrant: for densities in the range
$\rho_{c,<} < \rho < \rho_c$, both small and large values of $p$ favor free
flow, while for intermediate values, a nonzero fraction of vehicles have speeds
$< v_{max}$. In addition to representing a more realistic description of
driving behavior, this change leads to a better understanding of the phase
transition in the original model. Our results suggest an unexpected connection
between traffic models and stochastic sandpiles.
