Fog computing is an emerging paradigm that brings computing capabilities closer to distributed IoT devices, which provides networking services between end devices and traditional cloud data centers. One important mission is to further reduce the monetary cost of fog resources while meeting the ever-growing demands of multiple users. In this paper, we focus on minimizing the total cost for multiple mobile users to provide an efficient resource provisioning scheme in fog computing. The total cost includes two aspects: the replication cost and the transmission cost. We consider three cases for the resource provision problem by focusing on different cost models. First, one simple case where users can only upload one replication is discussed, and an optimal solution is proposed by converting the original problem into a bipartite graph matching. Then we consider a more complicated case in which each user can upload multiple replications on fog nodes in the resource provisioning. Specifically, two models are discussed: the 0–1 transmission cost model and the different transmission cost model. For the 0–1 transmission cost model, each user can upload multiple replications with a constant transmission cost, and one optimal greedy solution is proposed. For the different transmission cost model, the transmission cost is related to the distance of each pair of fog nodes. This problem is proven to be NP-hard. We first propose a non-adaptive algorithm which is proved to be bounded by $\frac{2}{3}W+\frac{1}{3}OPT$. Another $3+ϵ$-approximation algorithm is proposed based on local search, which has better performance with higher complexity. Extensive simulations also prove the efficiency of our schemes.

雾计算是一种新兴的范例，它使计算功能更接近于分布式物联网设备，后者可在终端设备和传统云数据中心之间提供联网服务。一个重要的任务是，在满足多个用户不断增长的需求的同时，进一步降低雾气资源的货币成本。在本文中，我们致力于最小化多个移动用户的总成本，以在雾计算中提供有效的资源供应方案。总成本包括两个方面：复制成本和传输成本。通过关注不同的成本模型，我们考虑了三种情况的资源供应问题。首先，讨论了一个用户只能上传一个副本的简单情况，并通过将原始问题转换为二部图匹配提出了一种最佳解决方案。然后，我们考虑一种更为复杂的情况，其中每个用户都可以在资源供应中的雾节点上上传多个副本。具体来说，讨论了两个模型：0-1传输成本模型和不同的传输成本模型。对于0-1传输成本模型，每个用户可以以恒定的传输成本上载多个副本，并提出了一种最优的贪婪解决方案。对于不同的传输成本模型，传输成本与每对雾节点的距离有关。事实证明，这个问题很难解决。我们首先提出了一种非自适应算法，该算法被证明是有界的 0-1传输成本模型和不同的传输成本模型。对于0-1传输成本模型，每个用户可以上载具有恒定传输成本的多个副本，并提出了一种最优的贪婪解决方案。对于不同的传输成本模型，传输成本与每对雾节点的距离有关。事实证明，这个问题很难解决。我们首先提出了一种非自适应算法，该算法被证明是有界的 0-1传输成本模型和不同的传输成本模型。对于0-1传输成本模型，每个用户可以以恒定的传输成本上载多个副本，并提出了一种最优的贪婪解决方案。对于不同的传输成本模型，传输成本与每对雾节点的距离有关。事实证明，这个问题很难解决。我们首先提出了一种非自适应算法，该算法被证明是有界的$\frac{2}{3}\mathrm{w\; ^}+\frac{\mathrm{1个}}{3}ØPŤ$。另一个$3+ϵ$提出了一种基于局部搜索的近似算法，具有更好的性能和更高的复杂度。大量的仿真也证明了我们方案的有效性。