Single-electron transport properties, recently observed in MBE-grown gate-controlled quantum dots, are studied by a self-consistent approach to the Poisson-Schrodinger problem. The potential profile in the cylindrical device is found from the solution of the Poisson equation as a superposition of external voltages, Schottky barrier potential, double-barrier potential of AlGaAs/InGaAs layers, and potential of ionized donors in n-GaAs layers. A small perturbation of the cylindrical symmetry has been taken into account. It is shown that the distribution of the ionized donors is of crucial importance in determining the current-voltage characteristics of the device. For the few-electron quantum dots, we have calculated the positions of peaks of source-drain current I as functions of gate voltage V-g and source-drain voltage V-sd We have quantitatively described the shell-filling effects and reproduced the characteristic structure of Coulomb diamonds, i.e. the diamond-shaped regions in V-g-V-sd plane corresponding to the Coulomb blockade (I = 0). We have also performed calculations with an external magnetic field taken into account and obtained a very good quantitative agreement between the calculated and measured magnetic field behavior of the source-drain current at fixed V-sd approximate to 0 and varying V-g.