Fog computing is of particular interest to Internet of Things (IoT), where inexpensive simple devices can offload their computation tasks to nearby Fog Nodes. Online scheduling in such fog networks is challenging due to stochastic network states such as task arrivals, wireless channels and location of nodes. In this paper, we focus on the problem of optimizing computation offloading management, arrival data admission control and resource scheduling, in order to improve the overall system performance, in terms of throughput fairness, power efficiency, and average mean of queue backlogs. We investigate this problem for a fog network with homogeneous mobile Fog Nodes, serving multiple wireless devices, controlled by a Fog Control Node. By formulating the problem as a stochastic optimization problem, maximizing utility-power efficiency, defined as achievable utility per-unit power consumption, subject to queue backlog stability, we modify Lyapunov optimization techniques to deal with the fractional form of utility-power efficiency function. Then we propose an online utility-power efficient task scheduling algorithm, which is asymptotically optimal. Our online task scheduling algorithm can achieve the theoretical [O(1/V), O(V)] trade-off between utility-power efficiency and average mean of queue backlogs,

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