Recent studies have demonstrated how the competition for the finite pool of available gene expression factors has important effect on fundamental gene expression aspects. In this study, based on a whole-cell model simulation of translation in S. cerevisiae, we evaluate for the first time the expected effect of mRNA levels fluctuations on translation due to the finite pool of ribosomes. We show that fluctuations of a single gene or a group of genes mRNA levels induce periodic behavior in all S. cerevisiae translation factors and aspects: the ribosomal densities and the translation rates of all S. cerevisiae mRNAs oscillate. We numerically measure the oscillation amplitudes demonstrating that fluctuations of endogenous and heterologous genes can cause a significant fluctuation of up to 50% in the steady-state translation rates of the rest of the genes. Furthermore, we demonstrate by synonymous mutations that oscillating the levels of mRNAs that experience high ribosomal occupancy (e.g. ribosomal "traffic jam") induces the largest impact on the translation of the S. cerevisiae genome. The results reported here should provide novel insights and principles related to the design of synthetic gene expression circuits and related to the evolutionary constraints shaping gene expression of endogenous genes.