  Fog networks offer computing resources with varying capacities at different
distances from end users. A Fog Node (FN) closer to the network edge may have
less powerful computing resources compared to the cloud, but processing of
computational tasks in an FN limits long-distance transmission. How should the
tasks be distributed between fog and cloud nodes? We formulate a universal
non-convex Mixed-Integer Nonlinear Programming (MINLP) problem minimizing task
transmission- and processing-related energy with delay constraints to answer
this question. It is transformed with Successive Convex Approximation (SCA) and
decomposed using the primal and dual decomposition techniques. Two practical
algorithms called Energy-EFFicient Resource Allocation (EEFFRA) and
Low-Complexity (LC)-EEFFRA are proposed. They allow for successful distribution
of network requests between FNs and the cloud in various scenarios
significantly reducing the average energy cost and decreasing the number of
computational requests with unmet delay requirements.
