A simple transport theory of a one-dimensional chain of small devices is presented. The chain is comprised of potential barriers connected by short conductors. Electrical transport through the barriers is described in terms of the quantum reflection and transmission coefficients. The conductors, which are longer than the de Broglie wavelength but eventually shorter than the mean tree path, are discussed within the Boltzmann transport theory. By fitting the solutions of the Boltzmann equation with the boundary conditions imposed by reflection and transmission at barriers a complete solution for the chain can be obtained. As an application, the two-barrier structure is studied in detail. As an function of the conductor length the current shows interference type resonances associated with scattering damped multiple reflections. The properties of the ballistic transistor are determined from the model.