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Virtualized small cell networks (SCNs) integrated with mobile edge computing (MEC) is a promising paradigm to provide both wideband access and intensive computation economically for user equipments (UEs) in the scenario of multiple mobile virtual network operators and infrastructure providers. However, the model of offloading in this case is often of high complexity and lacks effective solution. In this paper, by jointly considering offloading, time slice and power allocation, we formulate the energy consumption reduction of the UEs in virtualized SCNs with MEC as a mixed integer nonlinear programming. Our aim is to minimize the total energy consumption of the UEs subject to minimum overall throughput of the network. To solve the problem efficiently, we convert it into a biconvex problem by adding auxiliary variable, which enables the derivation of an efficient iterative algorithm by two subproblems. Towards the first subproblem, we introduce local variables to handle the coupling constraint, and propose an alternating direction method of multipliers (ADMM)-based distributed algorithm, where the closed-form expressions of the optimal solutions in variables updating are derived. For the second subproblem, the closed-form expressions of the optimal solution is also derived. Finally, the effectiveness of the proposed algorithm is demonstrated by extensive simulations with different system configurations.

Distributed Green Offloading and Power Optimization in Virtualized Small Cell Networks With Mobile Edge Computing