Complex biological systems, such as the cell cycle control network, are shown to be robust against various perturbations. It is crucial to identify the interactions of the network that can contribute towards robust cell cycle behaviour. The proteins in the cell cycle control network are regulated at the level of synthesis, degradation and activity. A closer examination of the network reveals that most of the proteins are subjected to all three types of regulation. Such multiple layers of regulation most probably contribute towards the robust cell cycle behaviour against perturbations. In this work, we investigate such a hypothesis by subjecting our budding yeast cell cycle model to global parameter perturbations using pre-defined viability criteria. We systematically tested the global role of regulated transcription and targeted degradation of proteins in driving robust cell cycle oscillations. We demonstrate that targeted degradation of proteins in the budding yeast cell cycle model makes the cell cycle oscillations robust against perturbations even in the absence of regulated transcription. We show that regulated transcription plays a major role in controlling the period of the cell cycle oscillations which is argued to be important for balanced cell growth and division. We show that both regulated transcription and degradation are part of feedback loops in the network which ensure robust function against parametric variations that can arise from the mutations and/or variations in protein levels.