Abstract : We study the problem of putting in sleep mode devices of a backbone network, while limiting the number of times each device changes its power state (full power mode or sleep mode). Our aim is to limit the number of network configurations, i.e., the change of the current set of network devices at full power. We develop a model, based on random graph theory, to compute the energy saving given a traffic variation, QoS constraints, and the number of allowed network configurations. Results show that the energy savings with few configurations (two or three per day) are close to the maximum one, in which a new configuration is applied for each traffic matrix. Thus, we can conclude that a practical implementation of sleep mode strategies for network operators is to define, on the basis of typical traffic trend, few configurations to be activated in specific time instants.