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Fog computing is emerging as a promising paradigm to perform distributed,low-latency computation by jointly exploiting the radio and computing resourcesof end-user devices and cloud servers. However, the dynamic and distributedformation of local fog networks is highly challenging due to the unpredictablearrival and departure of neighboring fog nodes. Therefore, a given fog nodemust properly select a set of neighboring nodes and intelligently offload itscomputational tasks to this set of neighboring fog nodes and the cloud in orderto achieve low-latency transmission and computation. In this paper, the problemof fog network formation and task distribution is jointly investigated whileconsidering a hybrid fog-cloud architecture. The goal is to minimize themaximum computational latency by enabling a given fog node to form a suitablefog network and optimize the task distribution, under uncertainty on thearrival process of neighboring fog nodes. To solve this problem, a novel onlineoptimization framework is proposed in which the neighboring nodes are selectedby using a threshold-based online algorithm that uses a target competitiveratio, defined as the ratio between the latency of the online algorithm and theoffline optimal latency. The proposed framework repeatedly updates its targetcompetitive ratio and optimizes the distribution of the fog node'scomputational tasks in order to minimize latency. Simulation results show thatthe proposed framework can successfully select a set of neighboring nodes whilereducing latency by up to 19.25% compared to a baseline approach based on thewell-known online secretary framework. The results also show how, using theproposed framework, the computational tasks can be properly offloaded betweenthe fog network and a remote cloud server in different network settings.

An Online Optimization Framework for Distributed Fog Network Formation with Minimal Latency