The understanding of complex biological processes whose function requires the interaction of a large number of components is strongly improved by the construction of mathematical models able to capture the underlying regulatory wirings and to predict the dynamics of the process in a variety of conditions. Iterative rounds of simulations and experimental analysis generate models of increasing accuracy, what is called the systems biology approach. The cell cycle is one of the complex biological processes that benefit from this approach, and in particular budding yeast is an established model organism for these studies. The recent publication about the modeling of the G1/S transition of the budding yeast cell cycle under a systems biology analysis has highlighted in particular the implications of the cell size determination that impinge the events driving DNA replication. During the life cycle of eukaryotic cells, DNA replication is restricted to a specific time window, called the S phase, and several control mechanisms ensure that each DNA sequence is replicated once, and only once, in the period from one cell division to the next. Here we extend the analysis of the G1/S transition model by including additional aspects concerning the DNA replication process, in order to give a reasonable explanation to the experimental dynamics, as well as of specific cell cycle mutants. Moreover, we show the mathematical description of the critical cell mass (P(s)) that cells have to reach to start DNA replication, which value is modulated depending on the different activation of the replication origins. The sensitivity analysis of the influence that the kinetic parameters of the G1/S transition model have on the setting of the P(s) value is also reported.