applications.

This paper is organized as follows: In Sec. \[model\_sec\] we define the models that are considered here and review some relevant results. Sec. \[sec-computer\] reports results for current and density profiles obtained by computer simulations. In Sec. \[sec-theory\] we develop a theoretical framework that helps us to understand the simulation results and the phase diagram. This theoretical approach is applied in Sec. \[sec-expval\] to compute the probability that a randomly chosen defect configuration exhibits phase separation. Finally, Sec. \[sec-summary\] gives a summary and conclusions.

Model and Definitions {#model_sec}
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We consider driven lattice gases with open boundary conditions and *Langmuir kinetics* (LK). To be more specific we focus on the TASEP which is believed to be a paradigmatic example for this class of dynamic processes. Here different extensions considering LK have been proposed, e.g. by including the diffusion of detached particles [@LipowskyKN01; @LipowskyK05]. We will focus on a less detailed model variant, the [*TASEP/LK*]{} [@pff1; @pff2], which is a TASEP with additional particle creation and annihilation in the bulk. The TASEP is defined on a lattice of $L$ sites which are numbered from $j=1$ to $j=L$ beginning at the left. Each site can be occupied by at most one 