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,

翻译：雾计算对物联网（IoT）具有特殊意义，其中廉价的简单设备可以将计算任务卸载到附近的雾节点。由于任务到达、无线信道和节点位置等随机网络状态，此类雾网络中的在线调度具有挑战性。在本文中，我们专注于优化计算卸载管理、到达数据准入控制和资源调度的问题，以在吞吐量公平性、功率效率和平均队列积压方面提高整体系统性能。我们针对一个由雾控制节点控制的、具有同构移动雾节点、服务多个无线设备的雾网络研究此问题。通过将该问题表述为一个随机优化问题，即在队列积压稳定性约束下最大化效用-功率效率（定义为可实现的效用与单位功耗之比），我们修改了Lyapunov优化技术以处理效用-功率效率函数的分数形式。然后，我们提出了一种在线效用-功率高效的任务调度算法，该算法是渐近最优的。我们的在线任务调度算法可以实现效用-功率效率与平均队列积压之间的理论[O(1/V), O(V)]权衡。