  We consider quantum random walks on congested lattices and contrast them to
classical random walks. Congestion is modelled with lattices that contain
static defects which reverse the walker's direction. We implement a dephasing
process after each step which allows us to smoothly interpolate between
classical and quantum random walkers as well as study the effect of dephasing
on the quantum walk. Our key results show that a quantum walker escapes a
finite boundary dramatically faster than a classical walker and that this
advantage remains in the presence of heavily congested lattices. Also, we
observe that a quantum walker is extremely sensitive to our model of dephasing.
