  The emerging 5G paradigm will enable multi-radio smartphones to run high-rate
stream applications. However, since current smartphones remain resource and
battery-limited, the 5G era opens new challenges on how to actually support
these applications. In principle, the service orchestration capability of the
Fog and Cloud Computing paradigms could be an effective means of dynamically
providing resource-augmentation to smartphones. Motivated by these
considerations, the peculiar focus of this paper is on the joint and adaptive
optimization of the resource and task allocations of mobile stream applications
in 5G-supported multi-tier Mobile-Fog-Cloud virtualized ecosystems. The
objective is the minimization of the computing-plus-network energy of the
overall ecosystem under hard constraints on the minimum streaming rate and the
maximum computing-plus-networking resources. To this end: 1) we model the
target ecosystem energy by explicitly accounting for the virtualized and
multi-core nature of the Fog/Cloud servers; 2) since the resulting problem is
non-convex and involves both continuous and discrete variables, we develop an
optimality-preserving decomposition into the cascade of a (continuous) resource
allocation sub-problem and a (discrete) task-allocation sub-problem; and 3) we
numerically solve the first sub-problem through a suitably designed set of
gradient-based adaptive iterations, while we approach the solution of the
second sub-problem by resorting to an ad-hoc-developed elitary Genetic
algorithm. Finally, we design the main blocks of EcoMobiFog, a technological
virtualized platform for supporting the developed solver. The extensive
numerical tests confirm that the energy-delay performance of the proposed
solving framework is typically within a few per-cent the benchmark one of the
exhaustive search-based solution.
