Edge computing techniques allow to exploit the devices at the network borders for computing efforts in order to reduce centralized cloud requests. A fog network is a feasible solution for implementing edge computing services. Within this scenario, the deployed fog nodes (FNs) are able to offload different portions of a single task to the available nodes to be processed at the network edge. However, to partially offload, FNs consume an extra amount of energy for transmission and reception of the tasks while saving energy by not processing the whole task on their own. Moreover, offloading requires an extra transmission and reception time to the task processing time. In this paper, the focus is on a partial offloading approach where the tradeoff between FN energy consumption and task processing delay is considered when estimating the portion to be offloaded to the available devices at the edge of the network by comparing a centralized and a distributed architecture. Simulation results demonstrate the effectiveness of the proposed estimation solutions in terms of FN energy consumption, average task delay, and network lifetime.