  We study a one-dimensional totally asymmetric simple exclusion process with
one special site from which particles fly to any empty site (not just to the
neighboring site). The system attains a non-trivial stationary state with
density profile varying over the spatial extent of the system. The density
profile undergoes a non-equilibrium phase transition when the average density
passes through the critical value 1-1/[4(1-ln 2)]=0.185277..., viz. in addition
to the discontinuity in the vicinity of the special site, a shock wave is
formed in the bulk of the system when the density exceeds the critical density.
