This thesis deals with stochastic transport of interacting particles. To model this kind of phenomena we employ the Totally Asymmetric Simple Exclusion Process (TASEP). TASEP was firstly proposed as a stochastic model for a biological transport process, that is the kinetics of protein synthesis from mRNA via the polyribosome. TASEP model is defined over a 1-dimensional lattice made of a large number of sites in which all particles can move only in one direction and each particle can hop from one site to its adjacent one, provided the latter is empty. In particular this model is characterized by the fact that the hopping rates are inhomogeneous - they are described by a function that varies continuously and slowly from site to site and has a single global minimum - and they depend also on the local configuration due to interactions between particles.