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We show that even though mobile networks are highly unpredictable when viewed at the individual node scale, the end-to-end quality-of-service (QoS) metrics can be stationary when the mobile network is viewed in the aggregate. We define the coherence time as the maximum duration for which the end-to-end QoS metric remains roughly constant, and the spreading period as the minimum duration required to spread QoS information to all the nodes. We show that if the coherence time is greater than the spreading period, the end-to-end QoS metric can be tracked. We focus on the energy consumption as the end-to-end QoS metric, and describe a novel method by which an energy map can be constructed and refined in the joint memory of the mobile nodes. Finally, we show how energy maps can be utilized by an application that aims to minimize a node's total energy consumption over its near-future trajectory.