An Analytical Model for Energy Minimization

Energy has emerged as a critical constraint in mobile computing because of the involving devices that are battery-operated with a limited amount of energy. We focus on the memory energy dissipa-tion. This is motivated by the fact that, for data intensive applications, a signiicant amount of energy is dissipated in the memory. Advanced memory architectures like the Mobile SDRAM and the RDRAM support multiple power states of memory banks, which can be exploited to reduce energy dissipation in the system. Therefore, it is important to design eecient controller policies that transition among power states. Since the addressed memory chip must be in the active state in order to perform a read/write operation, the key point is the tradeoo between the energy reduction of low power modes and the energy overheads of the resulting activations. The lack of a rigorous theoretical model for energy analysis is the main motivation of this paper. We consider the problem in a formal point of view and derive a model that captures the basis of the problem and the impact of available low power modes. Given a predetermined number of activations, we try to nd the optimal repartition among power modes, assuming a regular transition pattern. We evaluate our model on the RDRAM and analyze the behavior of each parameter together with the energy that can be save or loose.