In this thesis, we study two models related to the Total Asymmetric Simple Exclusion Process(TASEP) with Nearest Neighbor interaction, that are: - Facilitated Model - Antal-Schütz model The TASEP is a 1-D model defined on a linear chain with L sites. Every site can be occupied by almost one particle and the only possible action of our particle is a hop in the subsequent direction if the site is not occupied, with a rate defined by the system. This linear chain can be closed, this implies that the particle in site L hop in site 1 if not occupied, or open, that implies the particle can enter the system at site 1 and exit from the system at site L, with some rates.