  We study numerically the behavior of the Biham-Middleton-Levine traffic model
in three dimensions. Our extensive numerical simulations show that the phase
diagram for this model in three dimensions is markedly different from that in
one and two dimensions. In addition to the full speed moving as well as the
completely jamming phases, whose respective average asymptotic car speeds $<v>$
equal one and zero, we observe an extensive region of car densities $\rho$ with
a low but non-zero average asymptotic car speed. The transition from this
extensive low average asymptotic car speed region to the completely jamming
region is at least second order. We argue that this low speed region is a
result of the formation of a spatially-limited-extended percolating cluster.
Thus, this low speed phase is present in $n > 3$ dimensional
Biham-Middleton-Levine model as well.
