Proteins are large biological molecules that perform a vast array of functions within living organisms. Proteins are made from a process called translation, in which a ribosome decodes mRNA, a single-stranded copy of DNA, to produce a specific amino acid chain. Given the essential role of proteins in maintaining life, it is of central importance to comprehend the translation process and how it is regulated. Translation process can be divided into three major stages: initiation, elongation and termination. Regulation can occur at any of these stages to control protein production. In most cases, regulation primarily targets the initiation stage. Another direct mechanism to ensure accurate protein level in the cell is to regulate the stability of mRNA. Using mathematical modelling, in this thesis we investigate how protein production is controlled. We use a stochastic modelling approach called the Totally Asymmetric Simple Exclusion Process to model the translation process. Numerical simulation acts as a complementary tool. We first investigate how mRNA stability affects protein production from one mRNA during its lifetime. Next, we investigate auto-negative feedback on translation initiation and its substantial impact on controlling protein level in a cell. Finally, we incorporate ribosome recycling into the auto-negative feedback control. Novel results such as oscillation and bistable switching in protein level are found via this mathematical analysis. These predictions invite experimental testing.