  The asymmetric simple exclusion process with additional Langmuir kinetics,
i.e. attachment and detachment in the bulk, is a paradigmatic model for
intracellular transport. Here we study this model in the presence of randomly
distributed inhomogeneities ('defects'). Using Monte Carlo simulations, we find
a multitude of coexisting high- and low-density domains. The results are
generic for one-dimensional driven diffusive systems with short-range
interactions and can be understood in terms of a local extremal principle for
the current profile. This principle is used to determine current profiles and
phase diagrams as well as statistical properties of ensembles of defect
samples.
