  There is a continuous growth in demand for time sensitive applications which
has shifted the cloud paradigm from a centralized computing architecture
towards distributed heterogeneous computing platforms where resources located
at the edge of the network are used to provide cloud-like services. This
paradigm is widely known as fog computing. Virtual machines (VMs) have been
widely utilized in both paradigms to enhance the network scalability, improve
resource utilization, and energy efficiency. Moreover, Passive Optical Networks
(PONs) are a technology suited to handling the enormous volumes of data
generated in the access network due to their energy efficiency and large
bandwidth. In this paper, we utilize a PON to provide the connectivity between
multiple distributed fog units to achieve federated (i.e. cooperative)
computing units in the access network to serve intensive demands. We propose a
mixed integer linear program (MILP) to optimize the VM placement in the
federated fog computing units with the objective of minimizing the total power
consumption while considering inter-VM traffic. The results show a significant
power saving as a result of the proposed optimization model by up to 52%, in
the VM-allocation compared to a baseline approach that allocates the VM
requests while neglecting the power consumption and inter-VMs traffic in the
optimization framework.
