Fog networks offer computing resources of 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 the processing of computational tasks in 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 and their effectiveness is tested for various network and traffic scenarios. Using EEFFRA/LC-EEFFRA can significantly decrease the number of computational requests with unmet delay requirements when compared with baseline solutions (from 48% to 24% for 10 MB requests). Utilizing Dynamic Voltage and Frequency Scaling (DVFS) minimizes energy consumption (by one-third) while satisfying delay requirements.

Fog computing can be used to offload computationally intensive tasks from battery powered Internet of Things (IoT) devices. Although it reduces energy required for computations in an IoT device, it uses energy for communications with the fog. This paper analyzes when usage of fog computing is more energy efficient than local computing. Detailed energy consumption models are built in both scenarios with the focus set on the relation between energy consumption and distortion introduced by a Power Amplifier (PA). Numerical results show that task offloading to a fog is the most energy efficient for short, wideband links.