  Recent years have witnessed a remarkable development in communication and
computing systems, mainly driven by the increasing demands of data and
processing intensive applications such as virtual reality, M2M, connected
vehicles, IoT services, to name a few. Massive amounts of data will be
collected by various mobile and fixed terminals that will need to be processed
in order to extract knowledge from the data. Traditionally, a centralized
approach is taken for processing the collected data using large data centers
connected to a core network. However, due to the scale of the
Internet-connected things, transporting raw data all the way to the core
network is costly in terms of the power consumption, delay, and privacy. This
has compelled researchers to propose different decentralized computing
paradigms such as fog computing to process collected data at the network edge
close to the terminals and users. In this paper, we study, in a Passive Optical
Network (PON)-based collaborative-fog computing system, the impact of the
heterogeneity of the fog units capacity and energy-efficiency on the overall
energy-efficiency of the fog system. We optimized the virtual machine (VM)
placement in this fog system with three fog cells and formulated the problem as
a mixed integer linear programming (MILP) optimization model with the objective
of minimizing the networking and processing power consumption of the fog
system. The results indicate that in our proposed architecture, the processing
power consumption is the crucial element to achieve energy efficient VMs
placement.
