In this case the LIBA reduces to the SBA.

The LIBA neglects the influence of other defects on the transport capacity at site $x$. Nonetheless, we claim that the influence of other defects on the transport capacity can be considered as a perturbation in the same way as it is the case for the SBA in particle conserving systems [@GreulichS08]. Since the local attachment and detachment rates vanish in the continuum limit, the transport capacity of a bottleneck should be the same as in the corresponding particle conserving system. Therefore $J^*(x)$ is independent of $\Omega_a$ and $\Omega_d$. For the TASEP without LK analytical results are available [@GreulichS08; @bn_quasiexact] that can be used to obtain approximations for the transport capacity. Since the maximal current in these systams depends only on the bottleneck length $l(x)$ [@GreulichS08; @prot_prod_zia2] this holds also for the transport capacity. The concept of a local transport capacity is applicable if interactions of defects near a bottleneck are not to large and distances of defects are not too small (i.e. low defect density [^6]).

Hence, the transport capacity $J^*(x)$ yields an upper bound for the current profile, $$\label{init_cond_1}
J(x) \leq J^*(x) \hspace{5mm} \mbox{ for all $x$,}$$ while the function 