  Fog computing is an emerging paradigm that aims to improve the efficiency and
QoS of cloud computing by extending the cloud to the edge of the network. This
paper develops a comprehensive energy efficiency analysis framework based on
mathematical modeling and heuristics to study the offloading of virtual machine
(VM) services from the cloud to the fog. The analysis addresses the impact of
different factors including the traffic between the VM and its users, the VM
workload, the workload versus number of users profile and the proximity of fog
nodes to users. Overall, the power consumption can be reduced if the VM users
traffic is high and/or the VMs have a linear power profile. In such a linear
profile case, the creation of multiple VM replicas does not increase the
computing power consumption significantly (there may be a slight increase due
to idle / baseline power consumption) if the number of users remains constant,
however the VM replicas can be brought closer to the end users, thus reducing
the transport network power consumption. In our scenario, the optimum placement
of VMs over a cloud-fog architecture significantly decreased the total power
consumption by 56% and 64% under high user data rates compared to optimized
distributed clouds placement and placement in the existing AT&T network cloud
locations, respectively.
