Water is the most abundant molecule found in interstellar icy mantles. In space it is thought to be efficiently formed on the surfaces of dust grains through successive hydrogenation of O, O2 and O3. The underlying physico-chemical mechanisms have been studied experimentally in the past decade and in this paper we extend this work theoretically, using Continuous-Time Random-Walk Monte Carlo simulations to disentangle the different processes at play during hydrogenation of molecular oxygen. CTRW-MC offers a kinetic approach to compare simulated surface abundances of different species to the experimental values. For this purpose, the results of four key experiments-sequential hydrogenation as well as co-deposition experiments at 15 and 25 K-are selected that serve as a reference throughout the modeling stage. The aim is to reproduce all four experiments with a single set of parameters. Input for the simulations consists of binding energies as well as reaction barriers (activation energies). In order to understand the influence of the parameters separately, we vary a single process rate at a time. Our main findings are: (i) The key reactions for the hydrogenation route starting from O2 are H + O2, H + HO2, OH + OH, H + H2O2, H + OH. (ii) The relatively high experimental abundance of H2O2 is due to its slow destruction. (iii) The large consumption of O2 at a temperature of 25 K is due to a high hydrogen diffusion rate. (iv) The diffusion of radicals plays an important role in the full reaction network. The resulting set of 'best fit' parameters is presented and discussed for use in future astrochemical modeling.