  We present improvements of a recently introduced numerical method [Arrigoni
etal, Phys. Rev. Lett. 110, 086403 (2013)] to compute steady state properties
of strongly correlated electronic systems out of equilibrium. The method can be
considered as a non-equilibrium generalization of exact diagonalization based
dynamical mean-field theory (DMFT). The key modification for the
non-equilibrium situation consists in addressing the DMFT impurity problem
within an auxiliary system consisting of the correlated impurity, $N_b$
uncorrelated bath sites and two Markovian environments (sink and reservoir).
Algorithmic improvements in the impurity solver allow to treat efficiently
larger values of $N_b$ than previously in DMFT. This increases the accuracy of
the results and is crucial for a correct description of the physical behavior
of the system in the relevant parameter range including a semi-quantitative
description of the Kondo regime. To illustrate the approach we consider a
monoatomic layer of correlated orbitals, described by the single-band Hubbard
model, attached to two metallic leads. The non-equilibrium situation is driven
by a bias-voltage applied to the leads. For this system, we investigate the
spectral function and the steady state current-voltage characteristics in the
weakly as well as in the strongly interacting limit. In particular we
investigate the non-equilibrium behavior of quasi-particle excitations within
the Mott gap of the correlated layer. We find for low bias voltage Kondo like
behavior in the vicinity of the insulating phase. In particular we observe a
splitting of the Kondo resonance as a function of the bias voltage.
