Using cloud services from mobile devices has become a growing trend because of its mobility and convenience. However, mobile devices join and leave cloud services more frequently than traditional computers, which causes energy inefficiency in a cloud data center. Waste, in the form of energy and cooling requirements, particularly occurs when a mobile device disconnects from a service, but the cloud servers, known as virtual machines (VMs), continue running. The VMs should transition to lower-power states instead remaining active. However, transition to a lower-power state causes a service delay when users reconnect to the service because VMs in a lower-power state are not ready to serve. Therefore, an efficient energy policy must not only maximize energy savings but also minimize service delays. In this paper, we propose two approaches to energy efficiency: an Instant Energy Policy (IEP) that can quickly find an appropriate low-power state based on a predicted disconnection time and a Prediction-based Energy Policy (PrEP) that determines when to transition VMs to a low-power state and when to return them to the active state based on each users activity history. IEP predicts the unknown disconnection time using the multisize sliding windows workload estimation technique, which supports a non-stationary environment. This method can quickly obtain an energy policy, but it is limited when disconnection time fluctuates widely. PrEP presents an improved approach to achieve an optimal global result with respect to both energy consumption and service delay. Through simulations with a real-world dataset collected by the MIT Human Dynamics Lab, we show that PrEP provides approximately 20% power saving over the benchmark policies while guaranteeing minimal service delay.