  Stochastic driven flow along a channel can be modeled by the asymmetric
simple exclusion process. We confirm numerically the presence of a dynamic
queuing phase transition at a nonzero obstruction strength, and establish its
scaling properties. Below the transition, the traffic jam is macroscopic in the
sense that the length of the queue scales linearly with system size. Above the
transition, only a power-law shaped queue remains. Its density profile scales
as $\delta \rho\sim x^{-\nu}$ with $\nu={1/3}$, and $x$ is the distance from
the obstacle. We construct a heuristic argument, indicating that the exponent
$\nu={1/3}$ is universal and independent of the dynamic exponent of the
underlying dynamic process. Fast bonds create only power-law shaped depletion
queues, and with an exponent that could be equal to $\nu={2/3}$, but the
numerical results yield consistently somewhat smaller values $\nu\simeq
0.63(3)$. The implications of these results to faceting of growing interfaces
and localization of directed polymers in random media, both in the presence of
a columnar defect are pointed out as well.
