Fog computing is a promising architecture to provide economic and low latency data services for future Internet of things (IoT)-based network systems. It relies on a set of low-power fog nodes that are close to the end users to offload the services originally targeting at cloud data centers. In this paper, we consider a specific fog computing network consisting of a set of data service operators (DSOs) each of which controls a set of fog nodes to provide the required data service to a set of data service subscribers (DSSs). How to allocate the limited computing resources of fog nodes (FNs) to all the DSSs to achieve an optimal and stable performance is an important problem. In this paper, we propose a joint optimization framework for all FNs, DSOs and DSSs to achieve the optimal resource allocation schemes in a distributed fashion. In the framework, we first formulate a Stackelberg game to analyze the pricing problem for the DSOs as well as the resource allocation problem for the DSSs. Under the scenarios that the DSOs can know the expected amount of resource purchased by the DSSs, a many-to-many matching game is applied to investigate the pairing problem between DSOs and FNs. Finally, within the same DSO, we apply another layer of many-to-many matching between each of the paired FNs and serving DSSs to solve the FN-DSS pairing problem. Simulation results show that our proposed framework can significantly improve the performance of the IoT-based network systems.
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