Large-Scale Fog Computing Optimization using Equilibrium Problem with Equilibrium Constraints

Fog Computing potentially plays a pivotal role in delivering real-time data services to users, where large number of Fog Nodes (FNs) are deployed by various Data Service Operators (DSOs) to provide efficient services to the Authorized Data Service Subscribers (ADSSs). As a result, there exist tradings between DSOs and ADSSs in providing and purchasing these services, respectively. There also exists competition among all DSOs for providing these services at the prices that can maximize their profits. Moreover, competition exists among all ADSSs for purchasing the required amount of resources at the lowest available prices, and thus minimizing their costs. In this paper, we model the aforementioned competitions in fog computing as an Equilibrium Problem with Equilibrium Constraints (EPEC). In the EPEC, the DSOs provide incentives to the ADSSs and balance the utilities between the DSOs and the ADSSs. At the same time, the ADSSs leverage the incentives provided by the DSOs to their advantage. As the size of a typical fog computing network is large, the Alternating Direction Method of Multipliers (ADMM) algorithm, that has been recognized as a key method in large scale optimization can be employed. Utilizing the fast convergence and decomposition properties of ADMM, we achieve optimum results. Simulation results show that with the proposed framework, optimization of the utility functions of DSOs and ADSSs can be achieved in real-time. It is also shown that compared to the profit in traditional cloud computing and data center services, the total maximum profit of the ADSSs is improved to a great extent in fog computing.