In a fog-cloud environment, the tasks submitted by end-users are first sent to intermediate nodes called fog nodes. If the computing resources in fog nodes are insufficient, the nodes will offload tasks to the remote cloud. Naturally, intermediate nodes are reluctant to offload tasks to upstream entities, which in turn results in a degradation in network performance. To motivate such reluctant nodes, some previous studies have used game theoretical approaches. We believe that auction theory is one of the most important mathematical tools to motivate fog nodes to participate in offloading operations. In this paper, we propose a second-price sealed-bid auction mechanism to optimize offloading. In our model, the service unit plays the role of the commodity. Also, fog nodes and cloud datacenter play the role of bidders and auctioneers, respectively. We prove that the proposed auction mechanism has two important properties of incentive compatibility and incentive rationality. We formulate the problem using queuing theory in both the edge layer and the cloud layer. In each layer, the auction mechanism is used to allocate resources. We compare the proposed mechanism with state-of-the-art methods. Experimental evaluations using the iFogSim simulator indicated that the proposed method is much better than other methods in terms of significant criteria such as execution time, energy consumption, and network usage.

在雾云环境中，最终用户提交的任务首先被发送到称为雾节点的中间节点。如果雾节点中的计算资源不足，节点会将任务卸载到远程云端。自然地，中间节点不愿意将任务卸载到上游实体，这反过来会导致网络性能下降。为了激励这种不情愿的节点，之前的一些研究使用了博弈论方法。我们认为拍卖理论是激励雾节点参与卸载操作的最重要的数学工具之一。在本文中，我们提出了一种第二价格密封投标拍卖机制来优化卸载。在我们的模型中，服务单位扮演商品的角色。此外，雾节点和云数据中心分别扮演投标人和拍卖人的角色。我们证明了所提出的拍卖机制具有激励相容和激励合理性两个重要特性。我们在边缘层和云层都使用排队理论来制定问题。在每一层中，都使用拍卖机制来分配资源。我们将所提出的机制与最先进的方法进行比较。使用 iFogSim 模拟器的实验评估表明，在执行时间、能耗和网络使用等重要标准方面，所提出的方法比其他方法要好得多。我们将所提出的机制与最先进的方法进行比较。使用 iFogSim 模拟器的实验评估表明，在执行时间、能耗和网络使用等重要标准方面，所提出的方法比其他方法要好得多。我们将所提出的机制与最先进的方法进行比较。使用 iFogSim 模拟器的实验评估表明，在执行时间、能耗和网络使用等重要标准方面，所提出的方法比其他方法要好得多。