In this case we see a *shock* in the density profile which is characteristic for non-particle-conserving dynamics in the bulk and which cannot be observed in the particle conserving TASEP (except at $\alpha=\beta$).

![\[S-profs\](Colour online) Comparison of current and density profiles for $\alpha=0.1$ and $\beta=0.15$ (high density phase) in the homogeneous TASEP/LK and TASEP/LK with defects.](DP_S_def.eps "fig:"){width="0.9\columnwidth"}\
![\[S-profs\](Colour online) Comparison of current and density profiles for $\alpha=0.1$ and $\beta=0.15$ (high density phase) in the homogeneous TASEP/LK and TASEP/LK with defects.](Jprofs_S_def.eps "fig:"){width="0.9\columnwidth"}

Increasing the entry rate $\alpha$ for fixed and large $\beta$ one observes a queuing transition in Fig. \[phase\_sep\]: At a critical entry rate $\alpha^*$ the peak at the leftmost defect broadens, forming a high density region. This corresponds to phase separation and is also observed in the inhomogeneous TASEP at critical boundary rates. In the TASEP, however, the high density regime always extends to the left boundary. In contrast, the inhomogeneous TASEP/LK-system exhibits a *stationary* shock separating the low and high density region. Numerical finite-size scaling in Fig. \[finsize\_scale1\] shows that the shock is getting sharper with increasing system size. Thus the high density region extends over a finite fraction of the system, corresponding to phase separation. In contrast, 