In this thesis we use analytical methods and computer simulations to investigate the steady-state behaviour of a one-dimensional TASEP connected to two coupled reservoirs. The reservoirs have finite size, no internal dynamics and can interact with each other via simple diffusion. The system is closed and thus the total number of particles is conserved. We focus on analysing a situation of slow exchange between the reservoirs, i.e. the diffusion mechanism between the reservoirs and particle hopping inside the TASEP are comparable.