Modeling sleep modes gains with random graphs

Nowadays two main approaches are being pursued to reduce energy consumption of network devices: the use of sleep modes in which devices can be put in low-power state, and the adoption of energy proportional approaches where the device architecture is designed to make energy consumption proportional to the actual load. In this paper, we formulate a theoretical model based on random graph theory to estimate the potential gains that can be achieved by adopting sleep modes in networks where energy proportional devices are deployed. Is sleep mode still a winning approach in these scenarios? We consider a simple model of the energy consumption of network devices: a fixed cost represents the static consumption and a variable cost describes the linear proportionality to the traffic load. Our results show that sleep modes are effective also in presence of load proportional solutions, even if traffic has to be routed on longer paths, unless the static power consumption component is of the same order of magnitude of the load proportional component.