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In this paper, we investigate the energy efficient computation offloading scheme in a multi-user fog computing system. We consider the users need to make the decision on whether to offload the tasks to the fog node nearby, based on the energy consumption and delay constraint. In particular, we utilize queuing theory to bring a thorough study on the energy consumption and execution delay of the offloading process. Two queuing models are applied respectively to model the execution processes at the mobile device (MD) and fog node. Based on the theoretical analysis, an energy efficient optimization problem is formulated with the objective to minimize the energy consumption subjects to execution delay constraints. In order to address the formulated problem, an alternating direction method of multipliers (ADMM)-based distributed algorithm is proposed. Extensive simulation studies are conducted to demonstrate …