Mobile edge computing is emerging as the new solution for next generation mobile applications, which require very low latency and high computing resources. By offloading the computation intensive tasks to mobile edge (ME) hosts located in the radio access network, users could gain energy saving benefits at the user equipment. However, two key factors that determine the total computing resource requirement of a ME host are the user mobility and offloading tasks request patterns. As a large number of ME hosts with physical servers are going to be deployed within the radio access network, energy efficiency is a key challenge for mobile edge service providers in terms of environmental impacts and operational costs. Our objective is to minimize the total energy consumption of the ME host system without compromising the users' quality of service based on correlated mobility pattern. We proposed a method to select the suitable server class for ME host deployment based on offloading task request profile considering energy efficiency. Then, we developed three processes to minimize the total power consumption of the ME host based on single threshold utilization: (i) Virtual Machine (VM) migration process that selects the suitable VMs for migration in order to save energy without compromising the quality of service; (ii) VM placement process that finds the best server, which minimizes the energy consumption; (iii) Physical server activation process that is responsible for activating servers from sleep state based on the network traffic demand. We propose a queueing-triggered based approach to initiate processes (ii) and (iii) to minimize both queueing delay and energy consumption. We evaluated our proposed methodologies using correlated mobility pattern and the uniform workload offloading pattern. Our results show that up to 34.32% of the energy can be saved by carefully selecting the physical servers in a ME host and an average of 16.15% energy savings can be achieved in the ME system using our proposed method during peak hours.