DNA copy number alterations (CNAs) are known to be related to genetic diseases, including cancer. Our previous study proposed a stochastic model to investigate the relationship between copy number and gene expression values. The simulation results revealed that the relationship is not generally linear except when the ratio of transcription factor (TF) arrival rate to TF departure rate is large. However, only a transcription productive (ON) state was considered in the previous study. Under certain environmental conditions, the demand for mRNA is limited and hence the transcription is turned off and strictly regulated. In this study, an alternative (OFF) state of transcription is proposed, in which, bound TFs are assumed to be shut down, or unloaded, immediately after stimulating a transcription. Using the Laplace-Stieltjes transform and numerical analysis, the relationship between DNA copy number and gene expression level is evaluated. The stochastic models show that CNAs would potentially alter, or even reverse, the amplitude changes of gene expression levels between the productive (ON) state and the alternative (OFF) state.