This paper investigates the optimal design of a hierarchical cloud-fog&edge computing (FEC) network, which consists of three tiers, i.e., the cloud tier, the fog&edge tier, and the device tier. The device in the device tier processes its task via three computing modes, i.e., cache-assisted computing mode, cloud-assisted computing mode, and joint device-fog&edge computing mode. Specifically, the task corresponds to being completed via the content caching in the FEC tier, the computation offloading to the cloud tier, and the joint computing in the fog&edge and device tier, respectively. For such a system, an energy minimization problem is formulated by jointly optimizing the computing mode selection, the local computing ratio, the computation frequency, and the transmit power, while guaranteeing multiple system constraints, including the task completion deadline time, the achievable computation capability, and the achievable transmit power threshold. Since the problem is a mixed integer nonlinear programming problem, which is hard to solve with known standard methods, it is decomposed into three subproblems, and the optimal solution to each subproblem is derived. Then, an efficient optimal caching, cloud, and joint computing (CCJ) algorithm to solve the primary problem is proposed. Simulation results show that the system performance achieved by our proposed optimal design outperforms that achieved by the benchmark schemes. Moreover, the smaller the achievable transmit power threshold of the device, the more energy is saved. Besides, with the increment of the data size of the task, the lesser is the local computing ratio.
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